Laurent Gourvès

A Dynasearch Neighborhood for the Bicriteria Traveling Salesman Problem

In this paper we extend the dynasearch approach proposed by Congram, Potts and van de Velde [4, 17] in the context of multicriteria optimization for the bicriteria traveling salesman problem. The idea is to use local search with an exponential sized neighborhood which can be searched in polynomial time using dynamic programming and a rounding technique. Experimental results are presented to verify the quality of the proposed approach to obtain approximate Pareto curves for the bicriteria traveling salesman problem.

(Non)-approximability for the multi-criteria TSP (1, 2)

Many papers deal with the approximability of multi-criteria optimization problems but only a small number of non-approximability results, which rely on NP-hardness, exist in the literature. In this paper, we provide a new way of proving non-approximability results which relies on the existence of a small size good approximating set (i.e. it holds even in the unlikely event of P=NP). This method may be used for several problems but here we illustrate it for a multi-criteria version of the traveling salesman problem with distances one and two (TSP(1,2)). Following the article of Angel et al. (FCT 2003) who presented an approximation algorithm for the bi-criteria TSP(1,2), we extend and improve the result to any number k of criteria.

Complexity of paths, trails and circuits in arc-colored digraphs

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 Dc 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 Dc 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].

Strategic coloring of a graph

We study a strategic game where every node of a graph is owned by a player who has to choose a color. A players payoff is 0 if at least one neighbor selected the same color, otherwise it is the number of players who selected the same color. The social cost of a state is defined as the number of distinct colors that the players use. It is ideally equal to the chromatic number of the graph but it can substantially deviate because every player cares about his own payoff, whatever how bad the social cost is. Following a previous work done by Panagopoulou and Spirakis [1] on the Nash equilibria of the coloring game, we give worst case bounds on the social cost of stable states. Our main contribution is an improved (tight) bound for the worst case social cost of a Nash equilibrium, and the study of strong equilibria, their existence and how far they are from social optima.

Approximation algorithms for the bi-criteria weighted MAX-CUT problem

We consider a generalization of the classical max-cut problem where two objective functions are simultaneously considered. We derive some theorems on the existence and the non-existence of feasible cuts that are at the same time near optimal for both criteria. Furthermore, two approximation algorithms with performance guarantee are presented. The first one is deterministic while the second one is randomized.