Results 1  10
of
21
PolynomialTime Data Reduction for DOMINATING SET
 Journal of the ACM
, 2004
"... Dealing with the NPcomplete Dominating Set problem on graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to planar graphs has a socalled problem kernel of linear size, achiev ..."
Abstract

Cited by 65 (8 self)
 Add to MetaCart
(Show Context)
Dealing with the NPcomplete Dominating Set problem on graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to planar graphs has a socalled problem kernel of linear size, achieved by two simple and easy to implement reduction rules. Moreover, having implemented our reduction rules, first experiments indicate the impressive practical potential of these rules. Thus, this work seems to open up a new and prospective way how to cope with one of the most important problems in graph theory and combinatorial optimization.
CompressionBased FixedParameter Algorithms for Feedback Vertex Set and Edge Bipartization
, 2006
"... We show that the NPcomplete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O(c k ·m) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, ..."
Abstract

Cited by 47 (4 self)
 Add to MetaCart
We show that the NPcomplete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O(c k ·m) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant. We extend this to an algorithm enumerating all solutions in O(d k ·m) time for a (larger) constant d. As a further result, we present a fixedparameter algorithm with runtime O(2 k · m 2) for the NPcomplete Edge Bipartization problem, which asks for at most k edges to remove from a graph to make it bipartite.
FPT is Ptime extremal structure I
 Algorithms and Complexity in Durham 2005, Proceedings of the first ACiD Workshop, volume 4 of Texts in Algorithmics
, 2005
"... We describe a broad program of research in parameterized complexity, and hows this plays out for the MAX LEAF SPANNING TREE problem. ..."
Abstract

Cited by 28 (2 self)
 Add to MetaCart
We describe a broad program of research in parameterized complexity, and hows this plays out for the MAX LEAF SPANNING TREE problem.
A Structural View on Parameterizing Problems: Distance from Triviality
 In First International Workshop on Parameterized and Exact Computation, IWPEC 2004, LNCS Proceedings
, 2004
"... Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consid ..."
Abstract

Cited by 25 (12 self)
 Add to MetaCart
Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consider tractable special cases of generally hard problems and to introduce parameters that measure the distance from these special cases. In this paper we present several case studies of distance from triviality parameterizations (concerning Clique, Power Dominating Set, Set Cover, and Longest Common Subsequence) that exhibit the versatility of this approach to develop important new views for computational complexity analysis.
Algorithm Engineering for Optimal Graph Bipartization
, 2009
"... We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental results. The worstcase time complexity is improved. Based on new structural insights, we give a simplified correctness proof. This also allows us to establish a heuristic improvement that in particular speeds up the search on dense graphs. Our best algorithm can solve all instances from a testbed from computational biology within minutes, whereas established methods are only able to solve about half of the instances within reasonable time.
Simplicity is beauty: improved upper bounds for Vertex Cover
, 2005
"... Abstract — This paper presents an O(1.2738 k + kn)time polynomialspace algorithm for VERTEX COVER improving both the previous O(1.286 k +kn)time polynomialspace algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745 k k 4 + kn)time exponentialspace algorithm, by Chandran and Grandoni. M ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
(Show Context)
Abstract — This paper presents an O(1.2738 k + kn)time polynomialspace algorithm for VERTEX COVER improving both the previous O(1.286 k +kn)time polynomialspace algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745 k k 4 + kn)time exponentialspace algorithm, by Chandran and Grandoni. Most of the previous algorithms rely on exhaustive casebycase analysis, and an underlying conservative worstcasescenario assumption. The contribution of the paper lies in the extreme simplicity, uniformity, and obliviousness of the algorithm presented. Several new techniques, as well as generalizations of previous techniques, are introduced including: general folding, struction, tuples, and local amortized analysis. The algorithm also induces improvement on the upper bound for the INDEPENDENT SET problem on graphs of degree bounded by 6. I.
On the parameterized intractability of motif search problems
 Combinatorica
, 2006
"... We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k) · n c) fo ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k) · n c) for any function f of k and constant c independent of k. The problem can therefore be expected to be intractable, in any practical sense, for k ≥ 3. Our result supports the intuition that Closest Substring is computationally much harder than the special case of Closest String, although both problems are NPcomplete. We also prove W[1]hardness for other parameterizations in the case of unbounded alphabet size. Our W[1]hardness result for Closest Substring generalizes to Consensus Patterns, a problem of similar significance in computational biology. 1
Exact algorithms and applications for Treelike Weighted Set Cover
 JOURNAL OF DISCRETE ALGORITHMS
, 2006
"... We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
(Show Context)
We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “treelike.” That is, the subsets in C can be organized in a tree T such that every subset onetoone corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edgeweighted acyclic hypergraph. Our main result is an algorithm running in O(3 k ·mn) time where k denotes the maximum subset size, n: = S, and m: = C. The algorithm also implies a fixedparameter tractability result for the NPcomplete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.
Extending the tractability border for closest leaf powers
 In International Workshop on Graph Theoretical Concepts in Computer Science (WG), number 3787 in Lecture Notes in Computer Science
, 2005
"... The NPcomplete Closest 4Leaf Power problem asks, given an undirected graph, whether it can be modified by at most ℓ edge insertions or deletions such that it becomes a 4leaf power. Herein, a 4leaf power is a graph that can be constructed by considering an unrooted tree—the 4leaf root—with leave ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
The NPcomplete Closest 4Leaf Power problem asks, given an undirected graph, whether it can be modified by at most ℓ edge insertions or deletions such that it becomes a 4leaf power. Herein, a 4leaf power is a graph that can be constructed by considering an unrooted tree—the 4leaf root—with leaves onetoone labeled by the graph vertices, where we connect two graph vertices by an edge iff their corresponding leaves are at distance at most 4 in the tree. Complementing and “completing ” previous work on Closest 2Leaf Power and Closest 3Leaf Power, we show that Closest 4Leaf Power is fixedparameter tractable with respect to parameter ℓ. This gives one of the first and so far deepest positive algorithmic results in the field of “approximate graph power recognition”—note that for 5leaf powers even the complexity of the exact recognition problem is open. 1