Ultimate characterizations of the burst response of an interval searching algorithm: a study of a functional equation (original) (raw)
Related papers
2009
Interval graph is a very important subclass of intersection graphs and perfect graphs. It has many applications in different real life situations. The problems on interval graph are solved by using different data structures among them interval tree is very useful. During last decade this data structure is used to solve many problems on interval graphs due to its nice properties. Some of its important properties are presented here. Here we introduced some problems on interval graphs which are solved by using the data structure interval tree. A brief review of interval graph is also given here.
Interval Tree and its Applications1
Advanced Modeling and Optimization, 2009
Abstract. Interval graph is a very important subclass of intersection graphs and perfect graphs. It has many applications in different real life situations. The problems on interval graph are solved by using different data structures among them interval tree is very useful. ...
A class of problems that can be solved using interval algorithms
2011
The paper discusses several theoretical and implementational problems of interval branch-and-bound methods. A trial to define a class of problems that can be solved with such methods is done. Features and variants of the method are presented. Useful data structures and shared-memory parallelization issues are considered.
Space-Constrained Interval Selection
Arxiv preprint arXiv:1202.4326, 2012
We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an algorithm for the special case of proper intervals, achieving improved approximation ratio of 3/2. We complement these upper bounds by proving that they are essentially best possible in the streaming setting: it is shown that an approximation ratio of 2 − (or 3/2 − for proper intervals) cannot be achieved unless the space is linear in the input size. In passing, we also answer an open question of Adler and Azar [1] regarding the space complexity of constant-competitive randomized preemptive online algorithms for the same problem.
On the complexity of the robust spanning tree problem with interval data
Operations Research Letters, 2004
This paper studies the complexity of the robust spanning tree problem with interval data (RSTID). It shows that the problem is NP-complete, settling the conjecture of Kouvelis and Yu, and that it remains so for complete graphs or when the intervals are all [0; 1]. These results indicate that the di culty of RSTID stems from both the graph topology and the structure of the cost intervals, suggesting new directions for search algorithms.
Discrete Mathematics, 2004
We introduce the m-ary interval tree, a random structure that underlies interval division and simultaneous parking problems. Certain significant paths in the m-ary interval trees are considered. When appropriately normed, the length of these paths are shown to converge in distribution to a normal random variable. The work extends the study of incomplete binary interval trees in Itoh and Mahmoud (J. Appl. Probab. 40 (2003) 645). However, the extension is nontrivial, in the sense that the characterization in the m-ary case involves high-order differential equations, which is to be contrasted with the first-order differential equation that underlies the binary case, and in the sense that the path lengths exhibit oscillatory behavior for m 4, that does not exist in binary and ternary cases.
The interval count of interval graphs and orders: a short survey
Journal of the Brazilian Computer Society, 2011
The interval count problem determines the smallest number of interval lengths needed in order to represent an interval model of a given interval graph or interval order. Despite the large number of studies about interval graphs and interval orders, surprisingly only a few results on the interval count problem are known. In this work, we provide a short survey about the interval count and related problems. a graph and the number of its maximal cliques.
Deferred-query: An efficient approach for some problems on interval graphs
Networks, 1999
This paper introduces the idea of a deferred-query approach to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit, and maximum matching problems on interval graphs given n endpoint-sorted intervals. The previous best-known algorithms run in O(n log log n) or O(n ϩ m) time, where m is the number of edges in the corresponding interval graphs.
Algorithms for interval structures with applications
Theoretical Computer Science, 2013
We present new algorithms for two problems on interval structures that arise in computeraided manufacturing and in other areas. We give an O(Kn) time algorithm for the singlesource K-link shortest path problem on an interval graph with n weighted vertices, and two O(n) time algorithms for a generalized version of the optimal color-spanning problem for n points on a real line, where each point is assigned one of m colors (m ≤ n). A standard approach for solving the K-link shortest path problem would take O(Kn 2) time, and thus our result offers a linear time improvement. The previously best known algorithm for the optimal color-spanning problem in R 1 takes O(n) time and space. We provide two algorithms for a generalized version of this problem in which each color must appear a specified minimum number of times. One of these two solutions is suitable for an online processing of the (streaming) input points; it uses O(m) working space for the ordinary one-dimensional optimal color-spanning problem. We also show several applications of our algorithms in computer-aided manufacturing and in other areas.
Exploring the search space with intervals
2008
Institute of Physics, Polish Academy of Sciences, Warsaw, Polandemail: gutow@ifpan.edu.plAbstract. The term global optimization is used in several contexts. Most oftenwe are interested in finding such a point (or points) in many-dimensional searchspace at which the objective function’s value is optimal, i.e. maximal or minimal.Sometimes, however, we are also interested in stability of the solution, that is inits robustness against small perturbations. Here I present the original, interval-analysis-based family of methods designed for exhaustive exploration of the searchspace. The power of intervalmethods makes it possible toreach all mentioned goalswithin a single, unified framework.