Carlos Martinhon - Academia.edu (original) (raw)

Papers by Carlos Martinhon

The edge-recoloring cost of monochromatic and properly edge-colored paths and cycles

Theoretical Computer Science, 2015

An Improved Relax-and-Fix Algorithm for the Fixed Charge Network Design Problem with User-optimal Flow

Discrete Mathematics Theoretical Computer Science Dmtcs, 2012

In this paper we deal from an algorithmic perspective with different questions regarding properly... more In this paper we deal from an algorithmic perspective with different questions regarding properly edge-colored (or PEC) paths, trails and closed trails. Given a c-edge-colored graph G c , we show how to polynomially determine, if any, a PEC closed trail subgraph whose number of visits at each vertex is specified before hand. As a consequence, we solve a number of interesting related problems. For instance, given subset S of vertices in G c , we show how to maximize in polynomial time the number of S-restricted vertex (resp., edge) disjoint PEC paths (resp., trails) in G c with endpoints in S. Further, if G c contains no PEC closed trails, we show that the problem of finding a PEC s-t trail visiting a given subset of vertices can be solved in polynomial time and prove that it becomes NP-complete if we are restricted to graphs with no PEC cycles.

Publicado nos Anais (em CD-ROM) do XXXII Simpósio Brasileiro de Pesquisa Operacional (XXXII SBPO)... more Publicado nos Anais (em CD-ROM) do XXXII Simpósio Brasileiro de Pesquisa Operacional (XXXII SBPO), 10/2000

This paper deals with the existence and search of properly edge-colored paths/trails between two,... more This paper deals with the existence and search of properly edge-colored paths/trails between two, not necessarily distinct, vertices s and t in an edge-colored graph from an algo-rithmic perspective. First we show that several versions of the s − t path/trail problem have polynomial solutions including the shortest path/trail case. We give polynomial algorithms for finding a longest properly edge-colored path/trail between s and t for a particular class of graphs and characterize edge-colored graphs without properly edge-colored closed trails. Next, we prove that deciding whether there exist k pairwise vertex/edge disjoint properly edge-colored s − t paths/trails in a c-edge-colored graph G c is NP-complete even for k = 2 and c = Ω(n 2), where n denotes the number of vertices in G c . Moreover, we prove that these problems remain NP-complete for c-colored graphs containing no properly edge-colored cy-cles and c = Ω(n). We obtain some approximation results for those maximization prob...

: In the Prize-Collecting Traveling Salesman Problem (PCTSP) we have to determine a tour visiting... more : In the Prize-Collecting Traveling Salesman Problem (PCTSP) we have to determine a tour visiting each vertex in the graph at most one time. If a given vertex is selected then an associated prize is collected, if a vertex is unrouted a penalty must be paid. We want to minimize an objective function balancing between the travel cost and the total penalties in a such way that a sufficiently large prize is collected. In this paper we present an hybrid metaheuristic that combines Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neigboorhood Search procedure as a local search. Experimental results show that it is potentially a powerful heuristic device, since it greatly enhace different features of these two approaches. Key words: Greedy Randomized Adaptive Search Procedure - GRASP, Variable Neighborhood Search - VNS, Local Search. 1 Introduction In the Prize-Collecting Traveling Salesman Problem (PCTSP) a prize is acquired in every visited city and a penalty is ...

A Lagrangian relaxation based exact solution algorithm for the Vehicle Routing Problem is introdu... more A Lagrangian relaxation based exact solution algorithm for the Vehicle Routing Problem is introduced in this paper. Lower bounds are obtained by allowing exponentially many inequalities as candidates to Lagrangian dualization. Three different families of strong valid inequalities (each one with exponentially many elements) appear in the formulation used. For each family, violated inequalities are identified through separation procedures for points that define minimum K-Trees (i.e. the solutions to the underlying Lagrangian problems).

GRASP Metaheuristics to the Generalized Covering Tour Problem

Modelling, Identification and Control, 2001

ABSTRACT This paper presents a GRASP algorithm to solve a generalized version of the Covering Tou... more ABSTRACT This paper presents a GRASP algorithm to solve a generalized version of the Covering Tour Problem (CTP), named here as Generalized Covering Tour Problem (GCTP). The GCTP consists of finding a minimum length tour also through a subset of W , instead of only a subset of V .Inordertoimprove the proposed algorithm performance, this work also presents some reduction rules that meaningfully minimize the dimensions of the CTP instances. Being the CTP a NP-Hard problem, the use of reduction rules might give e#ectiveness to any exact and approximated methods

The Edge-Recoloring Cost of Paths and Cycles in Edge-Colored Graphs and Digraphs

Lecture Notes in Computer Science, 2013

A Relax and Fix Approach to Solve the Fixed Charge Network Design Problem with User-Optimal Flow

Communications in Computer and Information Science, 2015

Lecture Notes in Computer Science, 2010

We deal with different algorithmic questions regarding properly arc-colored s-t paths, trails and... more We deal with different algorithmic questions regarding properly arc-colored s-t paths, trails and circuits in arc-colored digraphs. Given an arc-colored digraph D c with c ≥ 2 colors, we show that the problem of maximizing the number of arc disjoint properly arc-colored s-t trails can be solved in polynomial time. Surprisingly, we prove that the determination of one properly arc-colored s-t path is NP-complete even for planar digraphs containing no properly arc-colored circuits and c = Ω(n), where n denotes the number of vertices in D c . If the digraph is an arc-colored tournament, we show that deciding whether it contains a properly arc-colored circuit passing through a given vertex x (resp., properly arc-colored Hamiltonian s-t path) is NP-complete, even if c = 2. As a consequence, we solve a weak version of an open problem posed in Gutin et. al. [17].

Lecture Notes in Computer Science, 2009

This paper deals with problems on non-oriented edge-colored graphs. The aim is to find a route be... more This paper deals with problems on non-oriented edge-colored graphs. The aim is to find a route between two given vertices s and t. This route can be a walk, a trail or a path. Each time a vertex is crossed by a walk there is an associated non-negative reload cost ri,j, where i and j denote, respectively, the colors of successive edges in this walk. The goal is to find a route whose total reload cost is minimum. Polynomial algorithms and proofs of NP-hardness are given for particular cases: when the triangle inequality is satisfied or not, when reload costs are symmetric (i.e. ri,j = rj,i) or asymmetric. We also investigate bounded degree graphs and planar graphs.

Gerando orientações acíclicas com algoritmos probabilísticos distribuídos

Pesquisa Operacional, 2005

... Sistemas e Computação / COPPE; Universidade Federal do Rio de Janeiro (UFRJ); Rio de Janeiro ... more ... Sistemas e Computação / COPPE; Universidade Federal do Rio de Janeiro (UFRJ); Rio de Janeiro RJ; glads@cos.ufrj.br; felipe@cos.ufrj ... Na Seção 3, apresentamos os algoritmos básicos de Calabrese/França [CAL 94] [CAL 97] e introduzimos um novo algoritmo de geração ...

In the Prize-Collecting Traveling Salesman Problem (PCTSP) we have to determine a tour visiting e... more In the Prize-Collecting Traveling Salesman Problem (PCTSP) we have to determine a tour visiting each vertex in the graph at most one time. If a given vertex is selected then an associated prize is collected, if a vertex is unrouted a penalty must be paid. We want to minimize an objective function balancing between the travel cost and the total

This paper discusses two new randomized (or probabilistic) distributed algorithms for the generat... more This paper discusses two new randomized (or probabilistic) distributed algorithms for the generation of acyclic orientations upon anonymous distributed systems of arbitrary topology. The set of algorithms is analysed both in terms of convergency and velocity of convergency. In particular, it is shown that the new algorithm called Alg- Arestas, under easily obtainable conditions, is able to produce acyclic orientations quasi instantaneously, i.e., in less than two (2) steps. Two applications of this form of symmetry breaking will be discussed: initialization of Scheduling by Edge Reversal (SER), a simple and powerful distributed scheduling algorithm, and; a strategy for distributed uploading in computer networks. Keywords─ anonymous systems, mutual exclusion, randomized distributed algorithms, symmetry breaking.

An improved derandomized approximation algorithm for the max-controlled set problem

RAIRO - Theoretical Informatics and Applications, 2011

A vertex i of a graph G=(V,E) is said to be controlled by M ⊆ V if the majority of the elements o... more A vertex i of a graph G=(V,E) is said to be controlled by M ⊆ V if the majority of the elements of the neighborhood of i (including itself) belong to M. The set M is a monopoly in G if every vertex i ∈ V is controlled by M. Given a set M ⊆ V and two graphs G 1=(V,E 1) and G 2=(V,E 2) where E 1 ⊆ E 2, the monopoly verification problem (mvp) consists of deciding whether there exists a sandwich graph G=(V,E) (i.e., a graph where E 1 ⊆ E ⊆ E 2) such that M is a monopoly in G=(V,E). If the answer to the mvp is No, we then consider the max-controlled set problem (mcsp), whose objective is to find a sandwich graph G=(V,E) such that the number of vertices of G controlled by M is maximized. The mvp can be solved in polynomial time; the mcsp, however, is NP-hard. In this work, we present a deterministic polynomial time approximation algorithm for the mcsp with ratio \frac12+ \frac1+Ö&lt;/font &gt;n2n-&lt;/font &gt;2\frac{1}{2}+ \frac{1+\sqrt{n}}{2n-2}, where n=|V|&gt;4. (The case n ≤ 4 is solved exactly by considering the parameterized version of the mcsp.) The algoritm is obtained through the use of randomized rounding and derandomization techniques, namely the method of conditional expectations. Additionally, we show how to improve this ratio if good estimates of expectation are obtained in advance.