Shortest Path Problem Research Papers (original) (raw)

The problem of finding the shortest path from a path or graph has been quite widely discussed. There are also many algorithms that are the solution to this problem. The purpose of this study is to analyze the Greedy, A-Star, and Dijkstra algorithms in the process of finding the shortest path. The author wants to compare the effectiveness of the three algorithms in the process of finding the shortest path in a path or graph. From the results of the research conducted, the author can conclude that the Greedy, A-Star, and Dijkstra algorithms can be a solution in determining the shortest path in a path or graph with different results. The Greedy algorithm is fast in finding solutions but tends not to find the optimal solution. While the A-Star algorithm tends to be better than the Greedy algorithm, but the path or graph must have complex data. Meanwhile, Dijkstra's algorithm in this case is better than the other two algorithms because it always gets optimal results.

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- Computer Science, Pathfinding, Shortest Path Problem

In India, many patients lost because they were unable to get to the hospital on time in the event of an accident. Therefore, we are developing an ambulance service application that will reduce the need to get to the hospital. The main task of this project is to reduce the time between the ambulance driver and the patient and this will save his life. When the user opens the user app on their Smartphone, they will enter a place to go, then search for a nearby ambulance. Two Smartphone, one for the user and the other for the ambulance driver. Traffic accidents in the city have made loss of life from accidents even more crucial. To implement this, we will introduce a system called the Automatic Ambulance Recovery System that uses algorithms to search for shorter distances. The main theme beyond this scheme is to provide a simple flow for the ambulance to get to hospitals on time and therefore minimize propitiation. The ambulance is regulated by the primary unit which provides the longest scanning route to the ambulance and this position of the ambulance and consequently reaches the hospital safely. The GPS server also decides the location of the accident location through the vehicle that encounters the accident, and then the server walks through the ambulance to the location. This project will be fully automated, so find the crash site and help get to the hospital on time. The proposed system is designed for this monitoring system for the transportation of patients in an emergency. The system will be useful to monitor the current position of the ambulance, it must be the closest position that the ambulance can reach at the accident site.

- by GRD JOURNALS
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- Internet of Things (IoT), Shortest Path Problem

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap , is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C , a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O ( m + n log C ). A two-level form of radix heap gives a bound of O ( m + n log C /log log C ). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O ( m + n a @@@@log C ). The best previously known bounds are O ( m + n log n ) using Fibonacci heaps alone and O ( m log log C ) using the priority queue structure of Van Emde Boas et al. [ 17].

- by Robert Tarjan
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- Computer Science, Algorithms, Design, Queueing theory

The complexity of integrated-circuit chips produced today makes it feasible to build inexpensive, special-purpose subsystems that rapidly solve sophisticated problems on behalf of a general-purpose host computer. This paper contributes to the design methodology of efficient VLSI algorithms. We present a transformation that converts synchronous systems into more time-efficient, systolic implementations by removing combinational rippling.

- by Charles Leiserson
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- Computer Science, Logic, Signal Processing, Broadcasting

In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time. Using a standard transformation, thjis approach yields an O(m log n (m + n log n)) algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n 2 /m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say n', is much less than m. In this case, the running time of the algorithm is O((m' + n)log n(m + n log n)).

- by James Orlin
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- Applied Mathematics, Time Use, Business and Management, Operations

In This work the efficient algorithm for optimal cargo transport of N types of containers with limited ship capacity, minimizing the transport costs, is being developed. It can be applied for transport planning on a voyage route with multiple loading ports and multiple ports of discharge. The problem is solved with network optimization approach that can be seen as the minimum cost multicommodity flow problem (MCMCF). The implemented algorithm is able to find appropriate load planning sequence and to ensure minimal loading, discharging and transshipment costs, but with fulfillment of cargo demands in a number of destination ports on the voyage route. Application of this efficient tool may significantly reduce transport costs and ensure maximal possible profit. It may improve the operation process in maritime transport technology.

- by Srećko Krile
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- Engineering, Transport Planning, Transportation Planning, Profitability

The image foresting transform (IFT) is a graph-based approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definition of the IFT, and a procedure to compute it-a generalization of Dijkstra's algorithm-with a proof of correctness. We also discuss implementation issues and illustrate the use of the IFT in a few applications.

- by Jorge Stolfi and +1
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- Information Systems, Algorithms, Computer Graphics, Artificial Intelligence

We consider a variant of the constrained shortest path problem, where the constraints come from a set of forbidden paths (arc sequences) that cannot be part of any feasible solution. Two solution approaches are proposed for this variant. The first uses Aho and Corasick's keyword matching algorithm to filter paths produced by a k-shortest paths algorithm. The second generalizes Martins' deviation path approach for the k-shortest paths problem by merging the original graph with a state graph derived from Aho and Corasick's algorithm. Like Martins' approach, the second method amounts to a polynomial reduction of the shortest path problem with forbidden paths to a classic shortest path problem. Its significant advantage over the first approach is that it allows considering forbidden paths in more general shortest path problems such as the shortest path problem with resource constraints. Ó 2004 Published by Elsevier B.V.

- by Daniel Villeneuve and +1
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- Multidisciplinary, Shortest Path Problem, Network Flow, Shortest Path

Let G = (N, A) be an undirected graph with n nodes and m arcs, a designated source node s and a sink node t. This paper addresses sensitivity analysis questions concerning the shortest s-t path (SP) problem in G and the maximum capacity s-t path (MCP) problem in G. Suppose that * P is a shortest s-t path in G with respect to a nonnegative distance vector c. For each arc e ∈ A, the lower SP tolerance of an arc e is the minimum non-negative value that the length of arc e can take (with all other arc lengths staying fixed) so that * P remains an optimal path.

In this article, modeling of shortest path routing problem with artificial neural network is considered. In order to make our
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The shortest path problem is considered from a computational point of view. Eight algorithms which solve the shortest path tree problem on directed graphs are presented, together with the results of wide-ranging experimentation designed to compare their relative performances on different graph topologies. The focus of this paper is on the implementation of the different data structures used in the algorithms. A "Pidgin Pascal" description of the algorithms is given, containing enough details to allow for almost direct implementation in any programming language. In addition, Fortran codes of the algorithms and of the graph generators used in the experimentation are provided on the diskette.

- by Giorgio Gallo and +1
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- Experimental Design, Network optimization, Data Structure, Fortran

This paper introduces a new type of constraints, related to schedule synchronization, in the problem formulation of aircraft fleet assignment and routing problems and it proposes an optimal solution approach. This approach is based on Dantzig–Wolfe decomposition/column generation. The resulting master problem consists of flight covering constraints, as in usual applications, and of schedule synchronization constraints. The corresponding subproblem is a shortest path problem with time windows and linear costs on the time variables and it is solved by an optimal dynamic programming algorithm. This column generation procedure is embedded into a branch and bound scheme to obtain integer solutions. A dedicated branching scheme was devised in this paper where the branching decisions are imposed on the time variables. Computational experiments were conducted using weekly fleet routing and scheduling problem data coming from an European airline. The test problems are solved to optimality. A detailed result analysis highlights the advantages of this approach: an extremely short subproblem solution time and, after several improvements, a very efficient master problem solution time.

- by Jacques Desrosiers
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- Air Transport, Multidisciplinary, Column Generation, European

The Lee path connection algorithm is probably the most widely used method for finding wire paths on printed circuit boards. It is shown that the original claim of generality for the path cost function is incorrect, and a restriction, called the pathconsistency property, is introduced. The Lee algorithm holds for those path cost functions having this property. Codings for the cells of the grid are proposed which will allow the correct operation of the algorithm under the most general path cost function, using the minimum number of states possible, six states per cell. Then methods for reducing the number of calculations by increasing the number of states are presented.

- by Frank Rubin
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- Distributed Computing, Computer Hardware, Heuristic Search, Computer Software

In this paper we present a prototype of decision aid system for the logical layout design of unit-head machines with rotary table. User can add and modify characteristics of the part to be machined, the constraints related to the design of spindle heads and working positions, as well as precedence constraints related to operations. The goal of this software tool is minimize the total number of working positions and spindle heads, while reaching a given cycle time and satisfying the above constraints. The proposed method to solve the problem is based on its reduction to a constrained shortest path problem.

- by Alexandre Dolgui
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- Cycle Time, Design optimization, Shortest Path Problem, Decision Systems

Laporan praktikum Riset Operasi: Shortes Path adalah salah satu permasalahan ‘mudah’ saat mempelajari materi tentang graph, yaitu dengan mencari cost dari jalur terpendek (jalur dengan cost terendah) dalam suatu graph. Ada beberapa algoritma yang dapat digunakan untuk memecahkan permasalahan ini, antara lain yang cukup terkenal adalah Bellman Ford dan Djikstra. Namun, masing-masing algoritma tersebut memiliki kelemahan dan kelebihan, semisal dari segi efisiensi antara Bellman Ford dan Djikstra yang lebih efisien adalah Djikstra, akan tetapi dalam beberapa kasus Bellman Ford lebih unggul yaitu jika salah satu cost dari edgenya ada yang bernilai negatif, hal ini disebabkan algoritma Djikstra hanya bisa dipakai jika semua cost dari edgenya tidak bernilai negatif. Kemudian maksimum flow, yaitu masalah bagaimana cara menentukan besarnya penugasan flow pada suatu jaringan kerja sehingga flow yang sampai ke tujuan maksimal. Penyelesaian masalah maksimum flow dapat lebih mudah dan efisien jika menggunakan algoritma. Dua algoritma yang sudah ada dan sering digunakan yaitu algoritma Lintasan Penambah dan algoritma Pelabelan Aka.

- by Rauzan Sumara
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- Shortest Path Problem, Maximum Flow, Shortest Path

A common algorithm to solve the shortest path problem (SPP) is the Dijkstra algorithm. In this paper, a generalized Dijkstra algorithm is proposed to handle SPP in an uncertain environment. Two key issues need to be addressed in SPP with fuzzy parameters. One is how to determine the addition of two edges. The other is how to compare the distance between two different paths with their edge lengths represented by fuzzy numbers. To solve these problems, the graded mean integration representation of fuzzy numbers is adopted to improve the classical Dijkstra algorithm. A numerical example of a transportation network is used to illustrate the efficiency of the proposed method.

- by Sankaran Mahadevan
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- Information Systems, Applied Mathematics, Fuzzy Numbers, Shortest Path Problem

Dalam penelitian ini data ruas jalan direpresentasikan dalam graf berarah dimana jarak dari setiap node digunakan sebagai bobot untuk pencarian rute dengan Algoritma Floyd-Warshall. Data jarak dari setiap ruas jalan didapatkan dari Google map dengan memperhitungkan longitude dan latitude pada setiap node. Google map merupakan layanan pemetaan online gratis yang disediakan google dengan tampilan secara digital dan dapat diakses menggunakan browser oleh semua orang. Algoritma Floyd-Warshall akan melakukan pencarian rute terpendek kemudian Google Map akan menampikan data hasil perhitungan tersebut berupa rute beserta kode trayek yang dapat digunakan sebagai referensi oleh penumpang. Analisis hasil yang diperhatikan pada penelitian ini adalah hasil jarak dan rute yang dilalui oleh angkutan kota yang dibandingkan dari pilihan " public transportation " pada google maps.

In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants. This chapter proposes a classification and a generic formulation for the SPPRCs, briefly discusses complex modeling issues involving resources, and presents the most commonly used SPPRC solution methods. First and foremost,

- by Guy Desaulniers
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- Column Generation, Vehicle routing, Shortest Path Problem

This paper deals with the generation of minimal risk paths for the road transportation of hazardous materials between an origin-destination pair of a given regional area. The main considered issue is the selection of paths that minimize the total risk of hazmat shipments while spreading the risk induced on the population in an equitable way. The problem is mathematically formulated, and two heuristic algorithms are proposed for its solution. Substantially, these procedures are modified versions of Yen's algorithm for the k-shortest path problem, which take into due consideration the risk propagation resulting from close paths and spread the risk equitably among zones of the geographical region in which the transportation network is embedded. Furthermore, a lower bound based on a Lagrangean relaxation of the given mathematical formulation is also provided. Finally, a series of computational tests, referring to a regional area is reported.

In this article we propose a new single‐source shortest‐path algorithm that achieves the same O(n · m) time bound as the Bellman‐Ford‐Moore algorithm but outperforms it and other state‐of‐the‐art algorithms in many cases in practice. Our... more

- by Ahmed Shokry
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- Algorithms, Combinatorics, Graph/Network Algorithms, The shortest path problems

Given two points in a plane, each with a prescribed direction of motion in it, the question being asked is to find the shortest smooth path of bounded curvature that joins them. The classical 1957 result by Dubins gives a sufficient set of paths (each consisting of circular arcs and straight line segments) which always contains the shortest path. The latter is then found by explicitly computing all paths on the list and then comparing them. This may become a problem in applications where computation time is critical, such as in real-time robot motion planning. Instead, the logical classification scheme considered in this work allows one to extract the shortest path from the Dubins set directly, without explicitly calculating the candidate paths. The approach is demonstrated on one of two possible cases that appear here-when the distance between the two points is relatively large (the case with short distances can be treated similarly). Besides computational savings, this result sheds light on the nature of factors affecting the length of paths in the Dubins problem, and is useful for further extensions, e.g. for finding the shortest path between a point and a manifold in the corresponding configuration space.

- by Andrei Shkel
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- Mechanical Engineering, Robotics, Computational Geometry, Real Time

The task of finding the shortest path has received researcher's attention over the past two decades. In this paper, we deal with finding the shortest path on a fuzzy weighted graph, that is vertices (or nodes) and edges (or links) remain crisp, but the edge weights will be fuzzy numbers. We propose an algorithm to deal with fuzzy shortest path problem. The algorithm first finds the shortest path length and then a similarity measure degree is taken to find out the shortest paths.

- by kiran yadav
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- Fuzzy Logic, Membership Function, Shortest Path Problem, Fuzzy Set

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-costs shortest-path problems can likewise be extended to a general algebraic setting, provided the problems’ ordered commutative semigroup satisfies one additional restriction. In addition to this general result, we also show how our algorithms can be modified to solve certain bottleneck shortest-path problems, even though the ordered commutative semigroup naturally associated with bottleneck problems does not satisfy our additional restriction. We show how our bottleneck shortest-path techniques can be used to obtain fast algorithms for a variant of Hirschberg and Larmore’s optimal paragraph formation problem, and a special case of the bottleneck traveling-salesman problem.

- by Leo Liberti
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- Information Systems, Applied Mathematics, Business and Management, ROAD NETWORK
- by Maria Serna
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- Vlsi Design, Scheduling, Algorithm, Multidisciplinary

In this paper, we deal with the solution of the multicriteria shortest path problem. In particular, we present a class of labeling methods to generate the entire set of Pareto-optimal path-length vectors from an origin node s to all other nodes in a multicriteria network. The proposed methods are supported theoretically by the principle of optimality and they are defined

The time-constrained shortest path problem is an important generalization of the shortest path problem. The basic feature in time-constrained shortest path problem is considering when a node in the network can be visited under some time constraints. In this paper, a label-setting shortest path algorithm will be proposed to use in the synchronized traffic-light networks which uses the waiting times for green light (node costs) as well as the required times to pass the streets (link costs) to calculate the optimal routes. Index Terms-Time Constrained shortest path problem, traffic light networks, waiting time for green light, time window

- by karim faez
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- Synchronization, Shortest Path Problem, Shortest Path, Classification Algorithms
- by Sonia Vivas
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- Mobile Computing, Information Systems Engineering, Real Time Systems, Mobile Device

The focus of this paper is on the tricriterion shortest path problem where two objective functions are of the bottleneck type, for example MinMax or MaxMin. The third objective function may be of the same kind or we may consider, for example, MinSum or MaxProd. Let p(n) be the complexity of a classical single objective algorithm responsible for this third function, where n is the number of nodes and m be the number of arcs of the graph. An O(m 2 p(n)) algorithm is presented that can generate the minimal complete set of Pareto-optimal solutions. Finding the maximal complete set is also possible. Optimality proofs are given and extensions for several special cases are presented. Computational experience for a set of randomly generated problems is reported.

- by Claudio Bornstein
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- Multidisciplinary, Shortest Path Problem, Objective function

The development of concepts derived from the generic approach to solving the problem of the shortest path resulted in numerous and various algorithms that appeared over the past decades. The studies on the most basic operation aimed at the determination of the shortest path between two given points in a graph (in other words, often a network) have resulted in sophisticated solutions designed for more and more demanding applications. Those include finding the sets of paths with the shortest distance between all pairs of nodes or searching for a shortest path tree. The aim of the present article is to give the reader an introduction to the problem of the shortest path and a detailed review of two groups of selected algorithms designed to solve particular problems. In the study described herein, different algorithms have been examined for their efficacy in their operation in directed graphs of different type represented in a well-defined data structure. The empirical simulation-based analysis proves that the performance varies among algorithms under investigation and allows to suggest, which methods ought to be used to solve specific variants of the shortest path problem and which algorithms should be avoided or used with caution.

- by Piotr Zwierzykowski and +1
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- The shortest path problems, Successive Shortest Path Algorithm, Shortest Path Problem, Shortest Path

The aim of this paper is to investigate the use of heuristic information to efficiently solve to optimality the robust shortest path problem. Starting from the exact algorithm proposed by Murty and Her, we describe how this algorithm can be enhanced by using heuristic rules and evaluation functions to guide the search. The efficiency of the proposed enhanced approach is tested over a range of random generated instances. Our computational results indicate that the use of heuristic criteria is able to speed up considerably the search and that the enhanced exact solution method outperforms the state-of-the-art algorithm proposed by Murty and Her in most of the instances.

- by maria elena bruni
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- Information Systems, Applied Mathematics, Heuristic Search, Robust optimization

Tree (SPT) problem. The presented algorithm is an improvement over a previously published work of the authors. The effort is put in to improve the running/execution time of the SPT problem. Introduced improvement is simple and easy to... more

- by sohail safdar
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- Mathematics, Graph Theory, Complexity Theory, Algorithm

This paper considers the Bicriteria Shortest Path Problem (BSP) with the two conflicting objectives, minimizing the transportation cost and the total travel time. Bicriteria Shortest Path Problems, are often NP-hard problems [1], since obtaining the set of efficient solutions to a BSP problem is more difficult than solving the corresponding single-objective problem. This paper proposes a Bicriteria Genetic Algorithm approach to solve bicriteria shortest path problem.

This paper explores the construction of a Markov decision process (MDP) from a predicate transition net representation of a planning problem, which can be optimised using dynamic programming methods. The construction methodology... more

- by Sanjeev Naguleswaran and +1
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- Information Systems, Applied Mathematics, Markov Decision Process, Dynamic programming

A Travelling Salesman Problem with Allocation, Time Window and Precedence Constraints (TSP-ATWPC) is considered. The TSP-ATWPC occurs as a subproblem of optimally sequencing a given set of port visits in a real bulk ship scheduling problem, which is a combined multi-ship pickup and delivery problem with time windows and multi-allocation problem. Each ship in the fleet is equipped with a flexible cargo hold that can be partitioned into several smaller holds in a given number of ways, thus allowing multiple products to be carried simultaneously by the same ship. The allocation constraints of the TSP-ATWPC ensure that the partition of the ship's flexible cargo hold and the allocation of cargoes to the smaller holds are feasible throughout the visiting sequence. The TSP-ATWPC is solved as a shortest path problem on a graph whose nodes are the states representing the set of nodes in the path, the last visited node and the accumulated cargo allocation. The arcs of the graph represent transitions from one state to another. The algorithm is a forward dynamic programming algorithm. A number of domination and elimination tests are introduced to reduce the state space. The computational results show that the proposed algorithm for the TSP-ATWPC works, and optimal solutions are obtained to the real ship scheduling problem.

- by K. Fagerholt and +1
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- Information Systems, Applied Mathematics, Business and Management, State Space

A new column generation based exact optimization approach for the vehicle routing and scheduling problem with semi soft time windows (VRPSSTW) is presented. Elementary shortest path problem with resource constraints and late arrival penalties is solved as a subproblem, which rises from the Dantzig–Wolfe decomposition method. Exact solutions of VRPSSTW and hard time windows variant are compared on Solomon’s benchmark instances as well as on an instance based on Tokyo road network. It was found that the VRPSSTW solution results in fewer routes thus overall costs are reduced and late arrival penalties contribute only a small fraction to total cost.

- by Eiichi Taniguchi
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- Applied Mathematics, Column Generation, Vehicle routing, ROAD NETWORK

The problem of identifying the shortest path along a road network is a fundamental problem in network analysis, ranging from route guidance in a navigation system to solving spatial allocation problems. Since this type of problem is solved so frequently, it is important to craft an approach that is as efficient as possible. Based upon past research it is generally accepted that several efficient implementations of the Dijkstra algorithm are the fastest at optimally solving the 'one-to-one' shortest path problem (Cherkassky, et al. 1996). We show that the most efficient, state-of-the-art implementations of Dijkstra can be improved by taking advantage of network properties associated with GIS-sourced data. The results of this paper, derived from tests of different algorithmic approaches on real road networks, will be extremely valuable for application developers and researchers in the GIS community.

This paper proposes a weighted double-heuristic search algorithm to find the shortest path between two points. It can be used in numerous fields such as graph theory, game theory, and network. This algorithm, called T*, uses a weighted and heuristic function as f(x) = α × t(x) + β × h1(x) + γ × h2(x). It selects the path which minimises f(x) where x is a current node on the path, t(x) is cost of the path from start to x, h1(x) is a heuristic to estimate the cost from x to the straight line passing through start and target, and h2(x) is a heuristic to estimate cost of the cheapest path from x to target. Furthermore, α, β, and γ indicate effective weights of each sub-function on f(x). T* algorithm is compared to the Greedy and A* algorithms in terms of hit rate and the number of processed nodes. Comparison results show that the proposed algorithm has a high efficiency compared to other algorithms.

- by Mohammad Samadi
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- Graphs Theory, Graph Theory, Graph/Network Algorithms, Heuristic Search

Constraint programming based column generation is a hybrid optimization framework recently proposed that uses constraint programming to solve column generation subproblems. In the past, this framework has been used to solve scheduling problems where the associated graph is naturally acyclic and has done so very efficiently. This paper attempts to solve problems whose graph is cyclic by nature, such as routing problems, by solving the elementary shortest path problem with constraint programming. We also introduce new redundant constraints which can be useful in the general framework. The experimental results are comparable to those of the similar method in the literature (Desrochers, Desrosiers, and Solomon, 1992) but the proposed method yields a much more flexible approach.

- by Gilles Pesant
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- Constraint Programming, Mathematical Sciences, Column Generation, Vehicle routing

The present paper deals with the problem of locating hubs for freight mobility in urban and suburban areas. In particular, we present a heuristic method that combines aspects coming from both classical simple plant location problems and shortest path ones on multimodal graphs. In the first phase of the proposed heuristics, we identify those nodes that could be attractive poles

- by Anna Sciomachen
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- Transportation Networks, Shortest Path Problem, Shortest Path, Location Problem

This paper presents an analysis of the problems faced while learning Inter-Domain transformations of problem solutions. Given the solution to a problem in one domain say Game Theory; one can slightly change it to solve a similar or even a completely different prob lem from another domain say Computational Biology. Our work focuses on a Grid Structure which is a

- by Yasser Hashmi and +1
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- Game Theory, Graph Theory, Computational Biology, Sequence alignment
- by Daniele Vigo
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- Applied Mathematics, Linear Programming, Routing, Transportation

DNA computing has emerged as an interdisciplinary field that draws together molecular biology, chemistry, computer science, and mathematics. The fundamental of this unconventional computation has been proven to solve weighted graph problems, such as the shortest path problem and the travelling salesman problem. One of the fundamental improvements in DNA computing is direct-proportional length-based DNA computing for the shortest path problem. Generally, in DNA computing, the DNA sequences used for the computation should be critically designed in order to reduce error that could occur during computation. In this paper, a procedure to design the DNA sequences for the direct-proportional length-based DNA computing is presented. The procedure includes DNASequenceGenerator, a graph-based approach for designing a set of good DNA sequences.

Synthesis Lectures on Communication Networks is an ongoing series of 50-to 100-page publications on topics on the design, implementation, and management of communication networks. Each lecture is a self-contained presentation of one topic by a leading expert. The topics range from algorithms to hardware implementations and cover a broad spectrum of issues from security to multiple-access protocols. The series addresses technologies from sensor networks to reconfigurable optical networks. The series is designed to: • Provide the best available presentations of important aspects of communication networks. • Help engineers and advanced students keep up with recent developments in a rapidly evolving technology. • Facilitate the development of courses in this field.

- by John Baras
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- Distributed Algorithms, Routing, Communication Network, Graph

We consider a multi-agent scheduling problem on a single machine in which each agent is responsible for his own set of jobs and wishes to minimize the total weighted completion time of his own set of jobs. It is known that the unweighted problem with two agents is NP-hard in the ordinary sense. For this case, we can reduce our problem to a Multi-Objective Shortest-Path (MOSP) problem and this reduction leads to several results including Fully Polynomial Time Approximation Schemes (FPTAS). We also provide an efficient approximation algorithm with a reasonably good worst-case ratio.

- by Michael Pinedo
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- Engineering, Scheduling, Information Processing, Mathematical Sciences

We consider two approaches that model timetable information in public transportation systems as shortestpath problems in weighted graphs. In the time-expanded approach every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the time-dependent approach the graph contains only one node per station. Both approaches have been recently

- by Christos Zaroliagis
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- Public Transport, Time Dependent, Shortest Path Problem, Shortest Path

O problema de roteirização e programação de veículos com restrições de janela de tempo, de duração da jornada e de capacidade dos veículos é do tipo NP-hard. Este trabalho descreve três heurísticas desenvolvidas para resolvê-lo, as quais se baseiam na relaxação Lagrangiana de parte das restrições. O problema relaxado resultante corresponde a um problema de caminho mínimo com janelas de tempo (PCMJT), o qual é ainda NP-hard para frotas com mais de um veículo. As heurísticas a ele aplicadas utilizam uma versão aprimorada do algoritmo de etiquetamento permanente para solução do PCMJT. As heurísticas foram validadas com base em conjuntos de problemas-teste com janelas de tempo apresentados na literatura. As heurísticas desenvolvidas apresentam um desempenho equivalente ou superior, em termos de qualidade das soluções, em comparação aos modelos testados da literatura. As heurísticas foram ainda aplicadas com sucesso a um problema real de distribuição urbana em São Paulo.

- by Nicolau D F Gualda
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- Lagrangian Relaxation, Shortest Path Problem, Capacity constraint

hagen (DIKU) from November 2005 to October 2008 under the supervision of Professor David Pisinger. I would like to thank Professors Guy Desaulniers and Jacques Desrosiers whom I visited for half year in Montreal, and had the opportunity to continue working with after I returned to Denmark. Also, I would like to thank my colleagues at DIKU for a good place to work, especially Mads Jepsen, Bjørn Petersen and my supervisor David Pisinger for the many good discussions, and Mette Gamst and Laurent Flindt Muller for proof reading some chapters in this thesis. Thanks.

- by David Pisinger
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- Branch and Bound, Branching Process, Lower Bound, Shortest Path Problem