Showing papers by "Michael R. Fellows published in 2003"
TL;DR: The Graph k-Cut problem, that of finding a set of edges of minimum total weight, in an edge-weighted graph, such that their removal from the graph results in a graph having at least k connected components, is shown to be hard for the parameterized complexity class W.
147 citations
19 Jun 2003
TL;DR: This survey reviews the basic notions of parameterized complexity, and describes some new approaches to designing FPT algorithms and problem reductions for graph problems.
Abstract: This survey reviews the basic notions of parameterized complexity, and describes some new approaches to designing FPT algorithms and problem reductions for graph problems.
106 citations
TL;DR: In this paper, the authors consider the problem of finding a common superobject of size bounded by |Σ|+r and the parameter is the pair (k, r) and show that without this restriction, both problems are harder than Directed Feedback Vertex Set, for which parameterized complexity is famously unresolved.
46 citations
Proceedings Article•
01 Jan 2003TL;DR: The Shortest Common Supersequence problem restricted to inputs consisting of a collection of p-sequences (pSCS) is NP-complete; it is proved that the sequence analog of MAST can be solved in polynomial time and fixed-parameter tractability for pSCS and pSCT is proved.
Abstract: Two natural kinds of problems about structured collections of symbols can be generally referred to as the LARGEST COMMON SUBOBJECT and the SMALLEST COMMON SUPEROBJECT problems. which we consider here as the dual problems of interest. For the case of rooted binary trees where the symbols occur as leaf-labels and a subobject is defined by label-respecting hereditary topological containment, both of these problems are NP-complete, as are the analogous problems for sequences (the well-known LONGEST COMMON SUBSEQUENCE and SHORTEST COMMON SUPERSEQUENCE problems). When the trees are restricted by allowing each symbol to occur as a leaf-label at most once (which we call a phylogenetic tree or p-tree), then the LARGEST COMMON SUBTREE problem, better known as the MAXIMUM AGREEMENT SUBTREE (MAST) problem, is solvable in polynomial time. We explore the complexity of the basic subobject and superobject problems for both sequences and binary trees when the inputs are restricted to p-trees and p-sequences (p-sequences are sequences where each symbol occurs at most once). We prove that the sequence analog of MAST can be solved in polynomial time. The SHORTEST COMMON SUPERSEQUENCE problem restricted to inputs consisting of a collection of p-sequences (pSCS) is NP-complete; we show NP-completeness of the analogous SMALLEST COMMON SUPERTREE problem restricted to p-trees (pSCT). We also show that both problems are hard for the parameterized complexity classes W[1] where the parameter is the number of input objects. We prove fixed-parameter tractability for pSCS and pSCT when the k input objects are restricted to be complete: every symbol of Σ occurs exactly once in each object and the question is whether there is a common superobject of size bounded by | Σ | + r and the parameter is the pair (k, r). We show that without this restriction, both problems are harder than DIRECTED FEEDBACK VERTEX SET, for which parameterized complexity is famously unresolved.
45 citations
TL;DR: It is shown that, in the general case, both these problems are hard for the parameterized complexity class W[1], and in the case where the set of precedence constraints can be modelled by a partial order of bounded width, the problems are fixed parameter tractable.
42 citations
30 Jul 2003
TL;DR: The goals of this survey are to Motivate the basic notions of parameterized complexity and give some examples to introduce the toolkits of FPT and W-hardness as concretely as possible for those who are new to these ideas.
Abstract: The goals of this survey are to: (1) Motivate the basic notions of parameterized complexity and give some examples to introduce the toolkits of FPT and W-hardness as concretely as possible for those who are new to these ideas. (2) Describe some new research directions, new techniques and challenging open problems in this area.
36 citations
Journal Article•
TL;DR: In this article, an FPT algorithm with running time of O(n 4 + 2 O(k) n 2.5 ) is described for the SET SPLITTING problem, parameterized by the number k of sets to be split.
Abstract: An FPT algorithm with a running time of O(n 4 + 2 O(k) n 2.5 ) is described for the SET SPLITTING problem, parameterized by the number k of sets to be split. It is also shown that there can be no FPT algorithm for this problem with a running time of the form 2 o(k) n c unless the satisfiability of n-variable 3SAT instances can be decided in time 2 o(n) .
29 citations
19 Jun 2003
TL;DR: An FPT algorithm with a running time of O(n 4 + 2 O(k) n 2.5) is described for the Set Splitting problem, parameterized by the number k of sets to be split.
Abstract: An FPT algorithm with a running time of O(n 4 + 2 O(k) n 2.5) is described for the Set Splitting problem, parameterized by the number k of sets to be split. It is also shown that there can be no FPT algorithm for this problem with a running time of the form 2 o(k) n c unless the satisfiability of n-variable 3SAT instances can be decided in time 2 o(n).
27 citations
TL;DR: This paper describes simple versions of such applications that have been used to give school-children and the general public a broad understanding of what can be achieved, and how.
Abstract: Modern cryptography can achieve levels of security and authentication that non-specialists find literally incredible. Techniques including information-hiding protocols, zero-knowledge proofs and public key cryptosystems can be used to support applications like digital signatures, digital cash, on-line poker and secure voting in ways that are provably secure--far more secure than the traditional systems they replace. This paper describes simple versions of such applications that have been used to give school-children and the general public a broad understanding of what can be achieved, and how. The material has been extensively and successfully used by the authors in schools, science festivals and with undergraduates, and even postgraduate specialists.
19 citations
25 Aug 2003
TL;DR: This paper attempts to present algorithms for some related graph parameters in a different more easily accessible manner, by showing that the algorithms can be obtained by a stepwise modification of a trivial hypothetical non-deterministic algorithm.
Abstract: This paper investigates algorithms for some related graph parameters. Each asks for a linear ordering of the vertices of the graph (or can be formulated as such), and there are constructive linear time algorithms for the fixed parameter versions of the problems. Examples are cutwidth, pathwidth, and directed or weighted variants of these. However, these algorithms have complicated technical details. This paper attempts to present these algorithms in a different more easily accessible manner, by showing that the algorithms can be obtained by a stepwise modification of a trivial hypothetical non-deterministic algorithm.
4 citations
Proceedings Article•
01 Jan 2003