Results 1 
7 of
7
Reflections on multivariate algorithmics and problem parameterization
 PROC. 27TH STACS
, 2010
"... Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and e ..."
Abstract

Cited by 24 (19 self)
 Add to MetaCart
Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the “parameter space” of computationally hard problems.
On Tractable Cases of Target Set Selection
"... We study the NPcomplete TARGET SET SELECTION (TSS) problem occurring in social network analysis. Complementing results on its approximability and extending results for its restriction to trees and bounded treewidth graphs, we classify the influence of the parameters “diameter”, “cluster edge delet ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We study the NPcomplete TARGET SET SELECTION (TSS) problem occurring in social network analysis. Complementing results on its approximability and extending results for its restriction to trees and bounded treewidth graphs, we classify the influence of the parameters “diameter”, “cluster edge deletion number”, “vertex cover number”, and “feedback edge set number ” of the underlying graph on the problem’s complexity, revealing both tractable and intractable cases. For instance, even for diametertwo split graphs TSS remains very hard. TSS can be efficiently solved on graphs with small feedback edge set number and also turns out to be fixedparameter tractable when parameterized by the vertex cover number, both results contrasting known parameterized intractability results for the parameter treewidth. While these tractability results are relevant for sparse networks, we also show efficient fixedparameter algorithms for the parameter cluster edge deletion number, yielding tractability for certain dense networks.
On cutwidth parameterized by vertex cover
"... Abstract. We study the Cutwidth problem, where input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two consecutive vertices of the layout. We give an algorithm for Cutwidth with run ..."
Abstract
 Add to MetaCart
Abstract. We study the Cutwidth problem, where input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two consecutive vertices of the layout. We give an algorithm for Cutwidth with running time O(2 k n O(1)). Here k is the size of a minimum vertex cover of the input graph G, and n is the number of vertices in G. Our algorithm gives a a O(2 n/2 n O(1) ) time algorithm for Cutwidth on bipartite graphs as a corollary. This is the first nontrivial exact exponential time algorithm for Cutwidth on a graph class where the problem remains NPcomplete. Additionally we show that Cutwidth parameterized by the size of the minimum vertex cover of the input graph does not admit a polynomial kernel unless CoNP ⊆ NP/poly. Our kernelization lower bound contrasts the recent result of Bodlaender et al.[ICALP 2011] that Treewidth parameterized by vertex cover does admits a polynomial kernel. 1
WellQuasiOrders in Subclasses of Bounded Treewidth Graphs and their Algorithmic Applications
"... Abstract. We show that three subclasses of bounded treewidth graphs are wellquasiordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertexcovers are well quasi ordered by the induced subgraph order, graphs with bounded feedbackvertexset are well quasi ord ..."
Abstract
 Add to MetaCart
Abstract. We show that three subclasses of bounded treewidth graphs are wellquasiordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertexcovers are well quasi ordered by the induced subgraph order, graphs with bounded feedbackvertexset are well quasi ordered by the topologicalminor order, and graphs with bounded circumference are well quasi ordered by the inducedminor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement. 1
Intractability; FixedParameter Tractability
"... Abstract. Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investiga ..."
Abstract
 Add to MetaCart
Abstract. Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the “parameter space ” of computationally hard problems.
Parameterized complexity results for 1safe Petri nets
"... Abstract. We associate a graph with a 1safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]hardness results for many problems about 1safe Petri nets. As a corollary, this proves a conjecture ..."
Abstract
 Add to MetaCart
Abstract. We associate a graph with a 1safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]hardness results for many problems about 1safe Petri nets. As a corollary, this proves a conjecture of Downey et. al. about the hardness of some graph pebbling problems. We consider the parameter benefit depth (that is known to be helpful in getting better algorithms for general Petri nets) and again give W[1]hardness results for various problems on 1safe Petri nets. We also consider the stronger parameter vertex cover number. Combining the well known automatatheoretic method and a powerful fixed parameter tractability (Fpt) result about Integer Linear Programming, we give a Fpt algorithm for model checking Monadic Second Order (MSO) formulas on 1safe Petri nets, with parameters vertex cover number and the size of the formula. 1
Tractable Parameterizations for the Minimum Linear Arrangement Problem
"... Abstract. The Minimum Linear Arrangement (MLA) problem asks to embed a given graph on the integer line so that the sum of the edge lengths of the embedded graph is minimized. Most layout problems are either intractable, or not known to be tractable, parameterized by the treewidth of the input graphs ..."
Abstract
 Add to MetaCart
Abstract. The Minimum Linear Arrangement (MLA) problem asks to embed a given graph on the integer line so that the sum of the edge lengths of the embedded graph is minimized. Most layout problems are either intractable, or not known to be tractable, parameterized by the treewidth of the input graphs. We investigate MLA with respect to three parameters that provide more structure than treewidth. In particular, we give a factor (1+ε)approximation algorithm for MLA parameterized by (ε, k), where k is the vertex cover number of the input graph. By a similar approach, we describe two FPT algorithms that exactly solve MLA parameterized by, respectively, the maxleaf and edgecliquecover numbers of the input graph. 1