Marc Demange

RMIT University | RMIT · Department of Mathematical and Geospatial Sciences

Wildfires are a persistent threat for both people and the environment. These events are increasingly frequent and destructive and require effective responses that take into account multiple constrains and conflicting goals. In this paper, the problem of wildfire management is addressed focusing on preventing measures to avoid the uncontrolled sprea...

In the last decade, wildfires have become wider and more destructive. Climate change and the growth of urban areas are among the main factors that increase the risk of large-scale fires. This risk can be lowered with preventive measures. Among them, firefighting lines are used to stop the fire spread and to offer a safe corridor where firefighting...

The Orienteering Problem with Time Window and Delay (\OPTiWinD) is a variant of the online orienteering problem. A series of requests appear in various locations while a vehicle moves within the territory to serve them. Each request has a time window during which it can be served and a weight which describes its importance. There is also a minimum...

In this paper we consider an online version of different colouring problems in overlap graphs, motivated by some stacking problems. The instance is a system of time intervals presented in non-decreasing order of the left endpoint. We consider the usual colouring problem as well as b-bounded colouring (colour class have a maximum capacity b) and the...

In the last decade, wildfires have become wider and more destructive. The climate change and the growth of urban areas may further increase the probability of incidence of large-scale fires. The risk of fire can be lowered with preventive measures. Among them, firefighting lines are used to stop the fire from spreading beyond them. Due to high cost...

The Orienteering Problem with Time Window and Delay (OPTiWinD) is a variant of the online orienteering problem. A series of requests appear in various locations while a vehicle moves within the territory to serve them. Each request has a time window during which it can be served and a weight which describes its importance. There is also a minimum d...

The Probabilistic p-Center problem under Pressure ( Min PpCP) is a variant of the usual Min p-Center problem we recently introduced in the context of wildfire management. The problem is basically to locate p shelters minimizing the maximum distance people will have to cover in order to reach one of these shelters to reach the closest accessible she...

The location of shelters in different areas threatened by wildfires is one of the possible ways to reduce fatalities in a context of an increasing number of catastrophic and severe wildfires. These shelters will enable the population in the area to be protected in case of fire outbreaks. The subject of our study is to determine the best place for s...

The Firefighter Problem (FP) is a graph problem originally introduced in 1995 to model the spread of a fire in a graph, which has attracted considerable attention in the literature. The goal is to devise a strategy to employ a given sequence of firefighters on strategic points in the graph in order to contain efficiently the fire (which spreads fro...

In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the Fractional Firefighter game where the amount of protection allocated to a vertex lies between 0 and 1. While most...

In the FIREFIGHTER problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the FRACTIONAL FIREFIGHTER game where the amount of protection allocated to a vertex lies between 0 and 1. While most...

In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the Fractional Firefighter game where the amount of protection allocated to a vertex lies between 0 and 1. We introdu...

Let $G$ be a graph whose each component has order at least 3. Let $s : E(G) \rightarrow \mathbb{Z}_k$ for some integer $k\geq 2$ be an improper edge coloring of $G$ (where adjacent edges may be assigned the same color). If the induced vertex coloring $c : V (G) \rightarrow \mathbb{Z}_k$ defined by $c(v) = \sum_{e\in E_v} s(e) \mbox{ in } \mathbb{Z}...

A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs when the number $k$ of colors is limited. We get results which differ surprisingly from the usual case where $k...

Given a graph together with a partition of its vertex set, the minimum selective coloring problem consists of selecting one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is minimum. The contribution of this paper is twofold. First, we investigate the complexity status of the minimum selecti...

Given a finite group and a set , we consider the different cosets of each cyclic group with . Then the -graph associated with and can be defined as the intersection graph of all these cosets. These graphs were introduced in Bretto and Faisant (2005) as an alternative to Cayley graphs: they still have strong regular properties but a more flexible st...

In this paper we present the Selective Graph Coloring Problem, a generalization of the standard graph coloring problem as well as several of its possible applications. Given a graph with a partition of its vertex set into several clusters, we want to select one vertex per cluster such that the chromatic number of the subgraph induced by the selecte...

Given a graph G and a positive integer K, the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than K. In this paper, we focus on the inverse chromatic number problem for certain classes of graphs. First, we discuss diverse possible versions and then focus on two...

In this paper, we consider the minimum maximal matching problem in some classes of graphs such as regular graphs. We show that the minimum maximal matching problem is NP-hard even in regular bipartite graphs, and a polynomial time exact algorithm is given for almost complete regular bipartite graphs. From the approximation point of view, it is well...

This chapter is the fruit of collaboration between the LAMSADE laboratory and Bouygues Télécom with the goal of solving problems linked to interconnecting their mobile telephone network and the France Télécom network. Two problems arise in the design of telecommunications networks: firstly, what network should be constructed to satisfy a given traf...

In this paper, we consider the selective graph coloring problem. Given an integer k >= 1 and a graph G = (V;E) with a partition V1; : : : ; Vp of V , it consists in deciding whether there exists a set V^* ‡ in G such that |V ‡ \cap Vi| = 1 for all i \in {1; : : : ; p}, and such that the graph induced by V^* ‡ is k-colorable. We investigate the comp...

We consider the constrained graph alignment problem which has applications in biological network analysis studies. Given two input graphs G1;G2, a pair of vertex mappings induces an edge conservation if the vertex pairs are adjacent in their respective graphs. In general terms the goal is to provide a one-to-one mapping between the vertices of the...

In this paper, we give a new characterization of equimatchable graphs that are graphs with all maximal matchings having the same size. This gives an O(n2m)O(n2m)-algorithm for deciding whether a general graph of order n and with m edges is equimatchable. An O(n4.5)O(n4.5) recognition algorithm based on the Gallai–Edmonds Decomposition already follo...

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we parameterize such a problem by various other parameters, some of which may be the values of optimal solutions to di...

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard"). A natural subject for investigation is what happens when we parameterize such a problem by the size of an optimal solution of a different problem. We provide a framework for doing such...

Graph Theory International audience Given a graph, finding the maximal matching of minimum size (MMM) and the induced matching of maximum size (MIM) have been very popular research topics during the last decades. In this paper, we give new complexity results, namely the NP-hardness of MMM and MIM in induced subgrids and we point out some promising...

The maximum induced matching problem is known to be APX-hard in the class of bipartite graphs. Moreover, the problem is also intractable in this class from a parameterized point of view, i.e. it is W[1]-hard. In this paper, we reveal several classes of bipartite (and more general) graphs for which the problem admits fixed-parameter tractable algori...

The uncapacitated swapping problem is defined by a graph consisting of n vertices, and m object types. Each vertex of the graph is associated with two object types: the one that it currently holds, and the one it demands. Each vertex holds or demands ...

This chapter is divided into two parts: firstly, it evokes polynomial inverse problems and discusses the solution methods associated with them, and, secondly, the chapter discusses various hard inverse problems. The chapter also allows us to tackle the general question of comparing, from an algorithmic complexity point of view, the initial problem...

This chapter is the fruit of collaboration between the LAMSADE laboratory and Bouygues Télécom with the goal of solving problems linked to interconnecting their mobile telephone network and the France Télécom network. Two problems arise in the design of telecommunications networks: firstly, what network should be constructed to satisfy a given traf...

At the heart of the approximate methods for Non-deterministic Polynomial-time hard (NP-hard) problems from nonprofit organisation (NPO) is polynomial approximation, which studies the extent to which polynomial algorithms can give absolute guarantees as to the quality of the solutions obtained. This chapter outlines this result, which uses the main...

We study complexity issues related to some coloring problems in grids: we examine in particular the case of List coloring, of Precoloring extension and of (p,q)(p,q)-List coloring, the case of List coloring in bipartite graphs where lists in the first part of the bipartition are all of size pp and lists in the second part are of size qq. In particu...

Editorial of the Special Issue of Discrete Applied Math.

In this paper, we consider the selective graph coloring problem. Given an integer k ≥ 1 and a graph G = (V,E) with a partition V1, . . . , Vp of V , it consists in deciding whether there exists a set V^* in G such that |V^* ∩ Vi| = 1 for all i ∈ {1, . . . , p}, and such that the graph induced by V^* is k-colorable. We investigate the complexity sta...

This editorial describes the special issue on ‘New combinatorial optimisation models for decision-making’ of the International Journal of Applied Management Science (IJAMS). It provides a short review of combinatorial optimisation applications in decision-making, specifies the aim of the special issue, and finally presents an overview of five paper...

In this paper1 we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance (a graph with n vertices) is revealed in t clusters, 2 ≤ t ≤ n . We first focus on an on-line version of the maximumweighted hereditary subgraph problem. Then, we deal with the particular case of the independent set...

We study inverse chromatic number problems in permutation graphs and in interval graphs. Given a fixed instance and a fixed integer K, the instance has to be modified as little as possible so that the newly obtained graph can be colored with K colors or less. We show that the inverse (p, k)-colorability problem (defined similarly) in permutation gr...

This paper aims to start an analytical study of the computational complexity of some online shunting problems. We analyze the following problem. Consider a train station consisting of a set of parallel tracks. Each track can be approached from one side only or from both sides and the number of trains per track may be limited or not. The departure t...

Introduction Related problems Preliminaries and notation Complexity and (in) approximability Graphs of Δ = 2 A 2-approximation algorithm for general graphs Bipartite graphs Conclusions Bibliography

We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove that min weighted node coloring is NP-hard in P8-free bipartite graphs, but polynomial for P5-...

We study the problem where a robot has to pick up items of different sizes which are stored along a corridor. A natural requirement is that the items have to be collected in decreasing order of their sizes. We deal with various systems according to the location of the Entry/Exit station where the robot unloads the collected items after each trip al...

M. Yannakakis and F. Gavril showed in [“Edge dominating sets in graphs”, SIAM J. Appl. Math. 38, 364–372 (1980; Zbl 0455.05047)] that the problem of finding a maximal matching of minimum size (MMM for short), also called Minimum Edge Dominating Set, is NP-hard in bipartite graphs of maximum degree 3 or planar graphs of maximum degree 3. Horton and...

We consider inverse chromatic number problems in interval graphs having the following form: we are given an integer K and an interval graph G = (V,E), associated with n = |V| intervals I i = ]a i ,b i [ (1 ≤ i ≤ n), each having a specified length s(I i ) = b i − a i , a (preferred) starting time a i and a completion time b i . The intervals are to...

We consider a track assignment problem in a train depot leading to an online bounded coloring problem on permutation graphs or on overlap graphs. For permutation graphs we study the competitiveness of a First Fit-based algorithm and we show it matches the competitive ratio of the problem. For overlap graphs, even the unbounded case does not admit a...

The inverse traveling salesman problem belongs to the class of "inverse combinatorial optimization" problems. In an inverse combinatorial optimization problem, we are given a feasible solution for an instance of a particular combinatorial optimization problem, and the task is to adjust the instance parameters as little as possible so that the given...

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A version of weighted coloring of a graph is introduced which is motivated by some types of scheduling problems: each node v of a graph G corresponds to some operation to be processed (with a processing time w(v)), edges represent nonsimultaneity requirements (incompatibilities). We have to assign each operation to one time slot in such a way that...

Given an instance of a weighted combinatorial optimization problem and its feasible solution, the usual inverse problem is to modify as little as possible (with respect to a fixed norm) the given weight system to make the giiven feasible solution optimal. We focus on its 0-1 version, which is to modify as little as possible the structure of the giv...

We study online partitioning of posets from a graph theoretical point of view, which is coloring and cocoloring in comparability graphs. For the coloring problem, we analyse the First-Fit algorithm and show a ratio of $O(\sqrt{n})$; furthermore, we devise an algorithm with a competitivity ratio of $\frac{\chi+1}{2}$. For the cocoloring problem, we...

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by allowing to use not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NP- hardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line gra...

In this paper1 we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance (a graph with n vertices) is revealed in t clusters, 2 ? t ? n . We first focus on an on-line version of the maximumweighted hereditary subgraph problem. Then, we deal with the particular case of the independent set...

In this paper, we study the on-line version of the bin-packing problem. We analyze the approximation behavior of an on-line bin-packing algorithm under an approximation criterion called differential ratio. We are interested in two types of results : the differential competitivity ratio guaranteed by the on-line algorithm and hardness results that a...

This paper is devoted to an oriented coloring problem moti- vated by a task assignment model. A recent result established the NP- completeness of deciding whether a digraph is k-oriented colorable; we extend this result to the classes of bipartite digraphs and circuit-free di- graphs. Finally, we investigate the approximation of this problem: both...

The (p,k)-coloring problems generalize the usual coloring problem by replacing stable sets by cliques and stable sets. Complexities of some variations of (p,k)-coloring problems (split-coloring and cocoloring) are studied in line graphs; polynomial algorithms or proofs of NP-completeness are given according to the complexity status. We show that th...

We study completeness in differential approximability classes. In differential approximation, the quality of an approximation algorithm is the measure of both how far is the solution computed from a worst one and how close is it to an optimal one. We define natural reductions preserving approximation and prove completeness results for the class of...

We obtain improved approximation ratios for problems of a broad class called weighted hereditary induced-subgraph maximization problems, in particular for the maximum independent set, maximum clique and maximum ℓ-colorable induced subgraph, as well as for the minimum coloring problem. We also study the minimum chromatic sum and show that its weight...

We present a short overview on polynomial approximation of NP-hard problems. We present the main approximability classes together with examples of problems belonging to them. We also describe the general concept of approximability preserving reductions together with a discussion about their capacities and their limits. Finally, we present a quick d...

The (p, k)-coloring problems generalize the usual coloring problem by replacing stable sets by cliques and stable sets. Complexities of some variations of (p, k)-coloring problems (split-coloring and cocoloring) are studied in line graphs; polynomial algorithms or proofs of NP-completeness are given according to the complexity status. We show that...

We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case where k=p in \cite{tidosplit} where some upper and lower bounds on the optimal value minimizing k...

Starting from a batch scheduling problem, we consider a weighted subcoloring in a graph G; each node v has a weight w(v); each color class S is a subset of nodes which generates a collection of node disjoint cliques. The weight w(S) is defined as . In the scheduling problem, the completion time is given by where S=(S1,...,Sk) is a partition of the...

We study the minimum vertex-covering problem under two on-line models corresponding to two different ways vertices are revealed. The former one implies that the input-graph is revealed vertex- by-vertex. The second model implies that the input-graph is revealed per clusters, i.e. per induced subgraphs of the final graph. Under the cluster-model, we...

We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove that min weighted node coloring is NP-complete in P 8-free bipartite graphs, but polynomia...

LNCS n°3106, http://dx.doi.org/10.1007/978-3-540-27798-9_32 The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where...

City logistic problems aim to use the existent city infrastructure to improve the transportations network for goods delivery to the city centres. In this work, we attempt to build a model for the transportation of goods in a city with existing tramlines. Each car being a rack where to store containers, we consider the problem of organizing the cont...

We consider a weighted version of the subcoloring problem that we call the hypocoloring problem: given a weighted graph G=(V,E;w) where w(v)≥ 0, the goal consists in finding a partition \({\cal S}=(S_1,\ldots,S_k)\) of the node set of G into hypostable sets and minimizing ∑\(_{i=1}^{k}\) w(S i ) where an hypostable S is a subset of nodes which gene...

We study completeness in differential approximability classes. In differential approximation, the quality of an approximation algorithm is the measure of both how far is the solution computed from a worst one and how close is it to an optimal one. The main classes considered are DAPX, the differential counterpart of APX, including the NP optimizati...

We study the approximability of three versions of the Steiner tree problem. For the first one where the input graph is only supposed connected, we show that it is not approximable within better than |V N−ε for any ε ε (0, 1), where V and N are the vertex-set of the input graph and the set of terminal vertices, respectively. For the second of the St...

We study on-line versions of maximum weighted hereditary subgraph problems for which the instance is revealed in two clusters. We focus on the comparison of these on-line problems with their respective off-line versions. In [3], we have reduced on-line versions to the off-line ones in order to devise competitive analysis for such problems. In this...

This paper is the continuation of the paper "Autour de nouvelles notions pour l'analyse des algorithmes d'approximation: Formalisme unifié et classes d'approximation" where a new formalism for polynomial approximation and its basic tools allowing an "absolute" (individual) evaluation the approximability properties of NP-hard problems have been pres...

This paper is the continuation of the paper "Autour de nouvelles notions pour l'analyse des algorithmes d'approximation: Formalisme unifie et classes d'approximation" where a new formalism for polynomial approximation and its basic tools allowing an "absolute" (individual) evaluation the approximability properties of NP-hard problems have been pres...

The main objective of the polynomial approximation is the development of polynomial time algorithms for NP-hard problems, these algorithms guaranteeing feasible solutions lying "as near as possible" to the optimal ones. This work is the fist part of a couple of papers where we introduce the key-concepts of the polynomial approx-imation and present...

In on-line computation, the instance of a problem is revealed step-by-step and one has, at the end of each step, to irrevocably decide on the part of the final solution dealing with this step. We first study the minimum vertex-covering problem under two on-line models corresponding to two different ways vertices are revealed. The former one implies...

A version of weighted coloring of a graph is introduced: each node υ of a graph G = (V,E) is provided with a positive integer weight w(υ) and the weight of a stable set S of G is w(S) = maxw(υ) : υ ∈ V ∩ S. A k-coloring S = (S 1, . . . , S k) of G is a partition of V into k stable sets S 1, . . . , S k and the weight of S is w(S 1) + . . . + w(S k...

In on-line computation, the instance of a problem is revealed step-by-step and one has, at the end of each step, to irrevocably decide on the part of the final solution dealing with this step. We first study the minimum vertex-covering problem under two on-line models corresponding to two different ways vertices are revealed. The former one implies...

We analyze the approximation behavior of some of the best-known polynomial-time approximation algorithms for bin-packing under an approximation criterion, called differential ratio, informally the ratio (n - apx(I))/(n - opt(I)), where n is the size of the input list, apx(I) is the size of the solution provided by an approximation algorithm and opt...

In a first time we draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results can be expressed within it. Next, we use...

We first study the competitivity ratio for the on-line version of the problem of finding a maximum-order induced subgraph satisfying some hereditary property, under the hypothesis that the input graph is revealed by clusters. Next, we focus ourselves on two of the most known instantiations of this problem, the maximum independent set and the maximu...

We first study the competitive ratio for the on-line version of the problem of finding a maximum-order induced subgraph satisfying some hereditary property, under the hypothesis that the input graph is revealed by clusters. Next, we focus ourselves on two of the most known instantiations of this problem: the maximum independent set and the maximum...

In a first time we draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results can be expressed within it. Next, we use...

We first motivate and define a notion of asymptotic differential approximation mTio. For this, we introduce a new class of problems called radial problems including in particular the hereditary ones. Next, we validate rile definition of rile asymptotic differential approximation ratio by proving positive, conditional and negative approximation resu...

The purpose of this paper is mainly to prove the following theorem: for every polynomial time algorithm running in time T(n) and guaranteeing standard-approximation ratio varrho for bin-packing, there exists an algorithm running in time O(nT(n)) and achieving differential-approximation ratio 2 − varrho for BP. This theorem has two main impacts. The...

We consider the polynomial approximation behavior of the problem of finding, in a graph with weighted vertices, a maximal independent set minimizing the sum of the weights. In the spirit of a work of Halldrson dealing with the unweighted case, we extend it and perform approximation hardness results by using a reduction from the minimum coloring pro...

We shape a formal framework for distinguishing the behaviour of constructive and non-constructive polynomial time approximation algorithms for NP optimization problems. We introduce a new class, called SubNPO (sub-problems of NPO), that includes NPO and also some other problems used in recent works. For this class, we define two types of approximat...

We devise an approximation-preserving reduction of expansion O between weighted and unweighted versions of a class of problems called weighted hereditary induced-subgraph maximisation problems. This allows us to perform a first improvement of the best approximation ratio for the weighted independent set problem.

We draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results can be expressed within it.

We analyze the approximation behaviour of some of the best-known polynomial time approximation algorithms for bin-packing under an approximation criterion, called differential ratio. This measure has originally been introduced by Ausiello, D'Atri and Protasi and more recently revisited, in a more systematic way, by the first and the third authors o...

We use a new approximation measure, the differential approximation ratio, to derive polynomial-time approximation algorithms for minimum set covering (for both weighted and unweighted cases), minimum graph coloring and bin-packing. We also propose differential-approximation-ratio preserving reductions linking minimum coloring, minimum vertex coveri...

We prove that the existence of a polynomial time-approximation algorithm (where < 1="" is="" a="" fixed="" constant)for="" a="" class="" of="" independent="" set="" problems,="" leads="" to="" a="" polynomial="" timeapproximation="" algorithm="" with="" approximation="" ratio="" strictly="" smallerthan="" 2="" for="" vertex="" covering,="" while=""...

We first define the notion of approximation chain and then we use it to obtain, in polynomial time, asymptotic approximation ratio of min{κ/μ, [κ′ log(logΔ)]/Δ} (where κ is a fixed positive constant, κ′ is a constant depending on κ, and Δ, μ are the maximum and the average degrees of the graph, respectively). This result essentially improves, from...

We first study a generalization of the König-Egervary graphs, the class of the κ-KE graphs, and propose an exact polynomial time algorithm solving maximum independent set problem in this class. Next, we show how this result can be efficiently used to devise polynomial time approximation algorithms with improved approximation ratios for the maximum...

In order to define a polynomial approximation theory linked to combinatorial optimization closer than the existing one, we first formally define the notion of a combinatorial optimization problem and then, based upon this notion, we introduce a notion of equivalence among optimization problems. This equivalence includes, for example, translation or...