Random Separation: A New Method for Solving Fixed-Cardinality Optimization Problems

Cai, Lilong; Chan, Sau Man; Chan, Siu On

doi:10.1007/11847250_22

Cited by 81 publications

(115 citation statements)

References 14 publications

Supporting

Mentioning

114

Contrasting

Order By: Relevance

“…Our algorithm is based on the random separation techniques introduced by Cai, Chan and Chan [8]. We complement this result by showing in Section 4 that Editing to a Graph of Given Degrees parameterized by k + d has no polynomial kernel unless NP ⊆ coNP /poly if {vertex deletion, edge addition} ⊆ S. This resolves an open problem by Mathieson and Szeider [17].…”

Section: Editing To a Graph Of Given Degreesmentioning

confidence: 68%

Editing to a Graph of Given Degrees

Golovach

2014

Parameterized and Exact Computation

View full text Add to dashboard Cite

We consider the Editing to a Graph of Given Degrees problem that asks for a graph G, non-negative integers d, k and a function δ : V (G) → {1, . . . , d}, whether it is possible to obtain a graph G ′ from G such that the degree of v is δ(v) for any vertex v by at most k vertex or edge deletions or edge additions. We construct an FPT-algorithm for Editing to a Graph of Given Degrees parameterized by d+k. We complement this result by showing that the problem has no polynomial kernel unless NP ⊆ coNP /poly.

show abstract

Section: Editing To a Graph Of Given Degreesmentioning

confidence: 68%

Editing to a Graph of Given Degrees

Golovach

2014

Parameterized and Exact Computation

View full text Add to dashboard Cite

show abstract

“…It has previously been shown that, using random separation, DkS can be solved in 2 O(∆k) time with one-sided error and constant error probability [6]. Our algorithm above applied to DkS runs in 2 O(log(∆)k) time.…”

Section: Lemmamentioning

confidence: 99%

“…It is, however, fixed-parameter tractable with respect to the combined parameter "maximum degree ∆ and k" [6]. Holzapfel et al [13] showed that DkS remains NP-hard, even when looking only for subgraphs with average degree at least 2+Ω(1/k 1− ) for 0 < < 2.…”

Section: Introductionmentioning

confidence: 99%

Finding Dense Subgraphs of Sparse Graphs

Komusiewicz

Sorge

2012

Parameterized and Exact Computation

View full text Add to dashboard Cite

Abstract. We investigate the computational complexity of the Densestk-Subgraph (DkS) problem, where the input is an undirected graph G = (V, E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on DkS by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density µ of the sought subgraph, DkS becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixedparameter algorithm for DkS with respect to the combined parameter "degeneracy of G and |V | − k". On the negative side, we find that DkS is W[1]-hard with respect to the combined parameter "solution size k and degeneracy of G". We furthermore strengthen a previous hardness result for DkS [Cai, Comput. J., 2008] by showing that for every fixed µ, 0 < µ < 1, the problem of deciding whether G contains a subgraph of density at least µ is W[1]-hard with respect to the parameter |V | − k.

show abstract

“…Our FPT algorithm uses the following connection with a vertex cover problem that is solvable by the random separation method of Cai, Chan and Chan [4].…”

Section: Dual Connectedness By Vertex Deletionmentioning

confidence: 99%

“…By Lemma 3, it suffices to find k vertices in T that cover exactly 2k edges. We use a modification of the random separation algorithm of Cai, Chan and Chan [4] for finding a subset of vertices to cover exactly k edges.…”

Section: Theorem 3 Dually Connected Deletion Is Np-complete and W[1]mentioning

confidence: 99%

Dual Connectedness of Edge-Bicolored Graphs and Beyond

Cai

2014

Mathematical Foundations of Computer Science 2014

Self Cite

View full text Add to dashboard Cite

Abstract. Let G be an edge-bicolored graph where each edge is colored either red or blue. We study problems of obtaining an induced subgraph H from G that simultaneously satisfies given properties for H's red graph and blue graph. In particular, we consider Dually Connected Induced Subgraph problem -find from G a k-vertex induced subgraph whose red and blue graphs are both connected, and Dual Separator problem -delete at most k vertices to simultaneously disconnect red and blue graphs of G.We will discuss various algorithmic and complexity issues for Dually Connected Induced Subgraph and Dual Separator problems: NP-completeness, polynomial-time algorithms, W[1]-hardness, and FPT algorithms. As by-products, we deduce that it is NP-complete and W[1]-hard to find k-vertex (resp., (n − k)-vertex) strongly connected induced subgraphs from n-vertex digraphs. We will also give a complete characterization of the complexity of the problem of obtaining a k-vertex induced subgraph H from G that simultaneously satisfies given hereditary properties for H's red and blue graphs.

show abstract

Random Separation: A New Method for Solving Fixed-Cardinality Optimization Problems

Cited by 81 publications

References 14 publications

Editing to a Graph of Given Degrees

Editing to a Graph of Given Degrees

Finding Dense Subgraphs of Sparse Graphs

Dual Connectedness of Edge-Bicolored Graphs and Beyond

Contact Info

Product

Resources

About