R. Giroudeau | Université de Montpellier (original) (raw)

Papers by R. Giroudeau

Given a simple undirected graph G = (V, E) and an integer k ≤ |V |, the sparsest k-subgraph probl... more Given a simple undirected graph G = (V, E) and an integer k ≤ |V |, the sparsest k-subgraph problem asks for a set of k vertices which induce the minimum number of edges. Whereas its special case independent set and many other optimization problems become polynomial-time solvable in chordal graphs, we show that sparsest k-subgraph remains NP-hard in this graph class.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific ... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. 2-cover definition for a coupled-tasks scheduling problem

In this paper we consider the classical combinatorial optimization graph partitioning problem wit... more In this paper we consider the classical combinatorial optimization graph partitioning problem with Sum-Max as objective function. Given a weighted graph G = (V,E) and a integer k, our objective is to find a k-partition (V1,..., Vk) of V that minimizes∑k−1 i=1 ∑k j=i+1maxu∈Vi,v∈Vj w(u, v), where w(u, v) denotes the weight of the edge {u, v} ∈ E. We prove, in addition to the NP and W [1] hardnesses (for the parameter k), that there is no ρ-approximation algorithm for any ρ ∈ O(n1−), given any fixed 0 < ≤ 1 (unless P = NP), improving the previous 1+ 1 k lower bound of [5]. Lastly, we present a natural greedy algorithm with an approximation ratio better than k/2

Given a simple undirected graph G = (V, E) and an integer k ≤ |V |, the k-sparsest subgraph probl... more Given a simple undirected graph G = (V, E) and an integer k ≤ |V |, the k-sparsest subgraph problem asks for a set of k vertices that induce the minimum number of edges. As a generalization of the classical independent set problem, k-sparsest subgraph cannot admit (unless P = N P) neither an approximation nor an FPT algorithm (parameterized by the number of edges in the solution) in all graph classes where independent set is N P-hard. Thus, it appears natural to investigate the approximability and fixed parameterized tractability of k-sparsest subgraph in graph classes where independent set is polynomial, such as subclasses of perfect graphs. In this paper, we first present a simple greedy tight 2-approximation algorithm in proper interval graphs, and then we use dynamic programming to design a PTAS in proper interval graph and an FPT algorithm in interval graphs (parameterized by the number of edges in the solution).

This paper introduces a scheduling problem with coupled-tasks in presence of a compatibility grap... more This paper introduces a scheduling problem with coupled-tasks in presence of a compatibility graph on a single processor. We investigate a specific configuration, in which the coupled-tasks possess an idle time equal to 2. The complexity of these problems will be studied according to the presence or absence of triangles in the compatibility graph. As an extended matching, we propose a polynomial-time algorithm which consists in minimizing the number of non-covered vertices, by covering vertices with edges or paths of length two in the compatibility graph. This type of covering will be denoted by 2-cover technique. According on the compatibility graph type, the 2-cover technique provides a polynomial-time rho-approximation algorithm with rho=13/12 (resp. rho=10/9) in absence (resp. presence) of triangles.

More and more parallel and distributed systems (cluster, grid and global computing) are both beco... more More and more parallel and distributed systems (cluster, grid and global computing) are both becoming available all over the world, and opening new perspectives for developers of a large range of applications including data mining, multimedia, and bio-computing. However, this very large potential of computing power remains largely unexploited this being, mainly due to the lack of adequate and efficient software tools for managing this resource. Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time. Of obvious practical importance, it has been the subject of extensive research since the early 1950's and an impressive amount of literature now exists. The theory dealing with the design of algorithms dedicated to scheduling is much younger, but still has a significant history. An application which will be scheduled on a parallel architecture may be represented by an acyclic graph G = (V, E) (or precedence graph) where V designates the...

More and more parallel and distributed systems (cluster, gr id and global computing) are both bec... more More and more parallel and distributed systems (cluster, gr id and global computing) are both becoming available all over the world, and open ing ew perspectives for developers of a large range of applications including da ta mining, multimedia, and bio-computing. However, this very large potential of computing power remains largely unexploited this being, mainly due to the la ck of adequate and efficient software tools for managing this resource. Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time . Of obvious practical importance, it has been the subject of extensive research since the early 1950’s and an impressive am ount of literature now exists. Thetheorydealing with the design of algorithms dedicated to scheduli ng is much younger, but still has a significant history. An application which will be scheduled on a parallel archite cture may be represented by an acyclic graph G = (V,E) (or precedence graph) where V designates the...

In this paper, we study a scheduling problem with compled-tasks in presence of incompatible const... more In this paper, we study a scheduling problem with compled-tasks in presence of incompatible constraint. We give complexity results and a polynomial-time approximation for a specific problem when the compatibility graph has different topologies.

Theoretical Computer Science, 2021

Abstract This work is devoted to the study of the Balanced Connected Subgraph Problem (BCS) from ... more Abstract This work is devoted to the study of the Balanced Connected Subgraph Problem (BCS) from a complexity, inapproximability and approximation point of view. The input is a graph G = ( V , E ) , with each vertex having been colored, “red” or “blue”; the goal is to find a maximum connected subgraph G ′ = ( V ′ , E ′ ) from G that is color-balanced (having exactly | V ′ | / 2 red vertices and | V ′ | / 2 blue vertices). This problem is known to be NP -complete in general but polynomial in paths and trees. We propose a polynomial-time algorithm for block graph. We propose some complexity results for bounded-degree or bounded-diameter graphs, and also for bipartite graphs. We also propose inapproximability results for some graph classes, including chordal, planar, or subcubic graphs.

Journal of Scheduling, 2018

Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 2000

Currently in the Royal Navy, any training feedback provided during a team training exercise at se... more Currently in the Royal Navy, any training feedback provided during a team training exercise at sea or in the full training simulator is delivered by a human instructor “as required”, with the majority of feedback provided in a post-exercise debrief. An automated embedded training system would enable the provision of feedback in real-time during a training session to be standardised, but could provide an almost unlimited amount of feedback. The aim of this research is therefore to identify the benefits of providing on-line feedback, and to develop guidelines for future advanced training systems. This paper describes work that has been carried out to identify existing feedback principles, and to evaluate their utility in the context of a complex, real-time computer-based task. A series of experiments was conducted using a simulation of elements of a Naval Anti-Air Warfare decision making task, with Naval operators as participants. This paper describes the experimental test-bed and pro...

Theoretical Computer Science, 2015

We explore in this paper some complexity issues inspired by the contig scaffolding problem in bio... more We explore in this paper some complexity issues inspired by the contig scaffolding problem in bioinformatics. We focus on the following problem: given an undirected graph with no loop, and a perfect matching on this graph, find a set of cycles and paths covering every vertex of the graph, with edges alternatively in the matching and outside the matching, and satisfying a given constraint on the numbers of cycles and paths. We show that this problem is NP -complete, even in planar bipartite graphs. Moreover, we show that there is no subexponential-time algorithm for several related problems unless the Exponential-Time Hypothesis fails. Lastly, we also design two polynomial-time approximation algorithms for complete graphs.

Lecture Notes in Computer Science, 2015

Lecture Notes in Computer Science, 2013

Third International Symposium on Parallel and Distributed Computing/Third International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks

Lecture Notes in Computer Science, 2012