On the parameterized complexity of multiple-interval graph problems

Fellows, Michael R.; Hermelin, Danny; Rosamond, Frances A.; Vialette, Stéphane

doi:10.1016/j.tcs.2008.09.065

Cited by 296 publications

(210 citation statements)

References 25 publications

Supporting

Mentioning

210

Contrasting

Order By: Relevance

“…We will provide a parameterized reduction from the Multi-Colored Clique (MCC) problem, which was proven to be W[1]-complete by Fellows et al [5]. In MCC we are given an undirected graph that is properly colored by k colors and the question is whether there is a size-k clique in this graph consisting of exactly one vertex from each color class.…”

Section: Hardness Resultsmentioning

confidence: 99%

What Makes Equitable Connected Partition Easy

Enciso

Fellows

Guo

et al. 2009

Parameterized and Exact Computation

Self Cite

View full text Add to dashboard Cite

Abstract. We study the Equitable Connected Partition problem, which is the problem of partitioning a graph into a given number of partitions, such that each partition induces a connected subgraph, and the partitions differ in size by at most one. We examine the problem from the parameterized complexity perspective with respect to the number of partitions, the treewidth, the pathwidth, the size of a minimum feedback vertex set, the size of a minimum vertex cover, and the maximum number of leaves in a spanning tree of the graph. In particular, we show that the problem is W[1]-hard with respect to the first four parameters (even combined), whereas it becomes fixed-parameter tractable when parameterized by the last two parameters. The hardness result remains true even for planar graphs. We also show that the problem is in XP when parameterized by the treewidth (and hence any other mentioned structural parameter). Furthermore, we show that the closely related problem, Equitable Coloring, is FPT when parameterized by the maximum number of leaves in a spanning tree of the graph.

show abstract

Section: Hardness Resultsmentioning

confidence: 99%

What Makes Equitable Connected Partition Easy

Enciso

Fellows

Guo

et al. 2009

Parameterized and Exact Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…We describe a parameterized reduction from the W[1]-hard MULTICOLORED CLIQUE problem [24]: Instance: An undirected graph H = (W, F ) with a proper vertex coloring c : V → {1, . .…”

Section: Theorem 5 the Problem Of Deciding Whether There Is A (D G)mentioning

confidence: 99%

Finding Supported Paths in Heterogeneous Networks

et al. 2015

View full text Add to dashboard Cite

Subnetwork mining is an essential issue in the analysis of biological, social and communication networks. Recent applications require the simultaneous mining of several networks on the same or a similar vertex set. That is, one searches for subnetworks fulfilling different properties in each input network. We study the case that the input consists of a directed graph D and an undirected graph G on the same vertex set, and the sought pattern is a path P in D whose vertex set induces a connected subgraph of G. In this context, three concrete problems arise, depending on whether the existence of P is questioned or whether the length of P is to be optimized: in that case, one can search for a longest path or (maybe less intuitively) a shortest one. These problems have immediate applications in biological networks and predictable applications in social, information and communication networks. We study the classic and parameterized complexity of the problem, thus identifying polynomial and NP-complete cases, as well as fixed-parameter tractable and W[1]-hard cases. We also propose two enumeration algorithms that we evaluate on synthetic and biological data.

show abstract

“…In order to show the W [1]-hardness, we present a parameterized reduction from the W [1]-complete k-Multicolored Independent Set problem [10,11]. The problem is to decide for a given k-coloring f for a graph G = (V, E) whether there exists a multicolored k-independent set, that is, a vertex subset…”

Section: Parameterized Complexitymentioning

confidence: 99%

Incremental List Coloring of Graphs, Parameterized by Conservation

Hartung

Niedermeier

2010

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Incrementally k-list coloring a graph means that a graph is given by adding stepwise one vertex after another, and for each intermediate step we ask for a vertex coloring such that each vertex has one of the colors specified by its associated list containing some of in total k colors. We introduce the "conservative version" of this problem by adding a further parameter c ∈ specifying the maximum number of vertices to be recolored between two subsequent graphs (differing by one vertex). This "conservation parameter" c models the natural quest for a modest evolution of the coloring in the course of the incremental process instead of performing radical changes. We show that the problem is NP-hard for k ≥ 3 and W [1]-hard when parameterized by c. In contrast, the problem becomes fixed-parameter tractable with respect to the combined parameter (k, c). We prove that the problem has an exponential-size kernel with respect to (k, c) and there is no polynomial-size kernel unless NP ⊆ coNP/poly. Finally, we provide empirical findings for the practical relevance of our approach in terms of a very effective graph coloring heuristic.

show abstract

On the parameterized complexity of multiple-interval graph problems

Cited by 296 publications

References 25 publications

What Makes Equitable Connected Partition Easy

What Makes Equitable Connected Partition Easy

Finding Supported Paths in Heterogeneous Networks

Incremental List Coloring of Graphs, Parameterized by Conservation

Contact Info

Product

Resources

About