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11
Approximation and Tidying -- A Problem Kernel for s-Plex Cluster Vertex Deletion
- ALGORITHMICA
, 2011
"... We introduce the NP-hard graph-based data clustering problem s-PLEX CLUSTER VERTEX DELETION, where the task is to delete at most k vertices from a graph so that the connected components of the resulting graph are s-plexes. In an s-plex, every vertex has an edge to all but at most s−1 other vertice ..."
Abstract
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Cited by 1 (1 self)
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vertices; cliques are 1-plexes. We propose a new method based on “approximation and tidying ” for kernelizing vertex deletion problems whose goal graphs can be characterized by forbidden induced subgraphs. The method exploits polynomial-time approximation results and thus provides a useful link between
Planar-F Deletion: Approximation, Kernelization and Optimal FPT Algorithms
"... Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F as a minor. F-Deletion is a generic problem and by selectin ..."
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Cited by 18 (8 self)
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Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F as a minor. F-Deletion is a generic problem
Hitting forbidden minors: Approximation and kernelization
- IN PROCEEDINGS OF THE 8TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2011
"... We study a general class of problems called F-Deletion problems. In an F-Deletion problem, we are asked whether a subset of at most k vertices can be deleted from a graph G such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number o ..."
Abstract
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Cited by 12 (6 self)
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of algorithmic results on the F-Deletion problem when F contains a planar graph. We give • a linear vertex kernel on graphs excluding t-claw K1,t, the star with t leves, as an induced subgraph, where t is a fixed integer. • an approximation algorithm achieving an approximation ratio of O(log 3/2 OPT), where OPT
Kernelization Through Tidying -- A Case Study Based on s-Plex Cluster Vertex Deletion
- PROC. 9TH LATIN
, 2010
"... We introduce the NP-hard graph-based data clustering problem s-Plex Cluster Vertex Deletion, where the task is to delete at most k vertices from a graph so that the connected components of the resulting graph are s-plexes. In an s-plex, every vertex has an edge to all but at most s − 1 other verti ..."
Abstract
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vertices; cliques are 1-plexes. We propose a new method for kernelizing a large class of vertex deletion problems and illustrate it by developing an O(k 2 s 3)-vertex problem kernel for s-Plex Cluster Vertex Deletion that can be computed in O(ksn 2) time, where n is the number of graph vertices
Finding transitive approximations of . . .
, 2009
"... In Bioinformatics, the task of hierarchically classifying diseases with noisy data recently led to studying the Transitivity Editing problem, which is to change a given digraph by adding and removing a minimum number of arcs such that the resulting digraph is transitive. We show that both Transitivi ..."
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Transitivity Editing and Transitivity Deletion, which does not allow the insertion of arcs, are NP-complete even when restricted to DAGs. We provide polynomial-time executable data reduction rules that yield an O(k²)-vertex kernel for general digraphs and an O(k)-vertex kernel for digraphs of bounded degree
Kernelization via Sampling with Applications to Dynamic Graph Streams
"... In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions and deletions) and distributed systems such as MapReduce. In ..."
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In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions and deletions) and distributed systems such as Map
A GENERALIZATION OF NEMHAUSER AND TROTTER’S LOCAL OPTIMIZATION THEOREM
, 2009
"... The Nemhauser-Trotter local optimization theorem applies to the NP-hard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter’s result to vertex deletion and graph packing problems, introducin ..."
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Cited by 9 (4 self)
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The Nemhauser-Trotter local optimization theorem applies to the NP-hard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter’s result to vertex deletion and graph packing problems
Fast Dynamic Graph Algorithms for Parameterized Problems∗
"... Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and q ..."
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maintain-ing an approximate solution which can be used to construct a small problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a corollary, we obtain a quasilinear-time (poly-nomial) kernelization algorithm for Cluster Vertex Deletion. Until now, only quadratic time kernelization
Clustering with partial information
, 2008
"... The Correlation Clustering problem, also known as the Cluster Editing problem, seeks to edit a given graph by adding and deleting edges to obtain a collection of vertex-disjoint cliques, such that the editing cost is minimized. The Edge Clique Partitioning problem seeks to partition the edges of a g ..."
Abstract
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Cited by 7 (1 self)
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The Correlation Clustering problem, also known as the Cluster Editing problem, seeks to edit a given graph by adding and deleting edges to obtain a collection of vertex-disjoint cliques, such that the editing cost is minimized. The Edge Clique Partitioning problem seeks to partition the edges of a
Results 1 - 10
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11
