Results 1  10
of
13
Random Algorithms for the Loop Cutset Problem
 Journal of Artificial Intelligence Research
, 1999
"... We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c ..."
Abstract

Cited by 81 (2 self)
 Add to MetaCart
We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c \Delta 6 k kn) steps, with probability at least 1 \Gamma (1 \Gamma 1 6 k ) c6 k , where c ? 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm, called WRA, often finds a loop cutset that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known. 1
Parameterized Computational Feasibility
 Feasible Mathematics II
, 1994
"... Many natural computational problems have input consisting of two or more parts. For example, the input might consist of a graph and a positive integer. For many natural problems we may view one of the inputs as a parameter and study how the complexity of the problem varies if the parameter is he ..."
Abstract

Cited by 61 (20 self)
 Add to MetaCart
Many natural computational problems have input consisting of two or more parts. For example, the input might consist of a graph and a positive integer. For many natural problems we may view one of the inputs as a parameter and study how the complexity of the problem varies if the parameter is held fixed. For many applications of computational problems involving such a parameter, only a small range of parameter values is of practical significance, so that fixedparameter complexity is a natural concern. In studying the complexity of such problems, it is therefore important to have a framework in which we can make qualitative distinctions about the contribution of the parameter to the complexity of the problem. In this paper we survey one such framework for investigating parameterized computational complexity and present a number of new results for this theory.
Beyond NPCompleteness for Problems of Bounded Width: Hardness for the W Hierarchy (Extended Abstract)
 In Proceedings of the 26th Annual ACM Symposium on the Theory of Computing
, 1994
"... The parameterized computational complexity of a collection of wellknown problems including: Bandwidth, Precedence constrained kprocessor scheduling, Longest Common Subsequence, DNA physical mapping (or Intervalizing colored graphs), Perfect phylogeny (or Triangulating colored graphs), Colored cutw ..."
Abstract

Cited by 57 (21 self)
 Add to MetaCart
The parameterized computational complexity of a collection of wellknown problems including: Bandwidth, Precedence constrained kprocessor scheduling, Longest Common Subsequence, DNA physical mapping (or Intervalizing colored graphs), Perfect phylogeny (or Triangulating colored graphs), Colored cutwidth, and Feasible register assignment is explored. It is shown that these problems are hard for various levels of the W hierarchy. In the case of Precedence constrained kprocessor scheduling the results can be interpreted as providing substantial new complexity lower bounds on the outcome of [OPEN 8] of the Garey and Johnson list. We also obtain the conjectured "third strike" against Perfect phylogeny.
The Parameterized Complexity of Some Problems in Logic and Linguistics (Extended Abstract)
 Proceedings Symposium on Logical Foundations of Computer Science (LFCS), SpringerVerlag, Lecture Notes in Computer Science
, 2002
"... March 1, 2002 Rodney G. Downey Department of Mathematics, Victoria University P.O. Box 600, Wellington, New Zealand downey@math.vuw.ac.nz Michael R. Fellows, Bruce M. Kapron and Michael T. Hallett Department of Computer Science, University of Victoria Victoria, British Columbia V8W 3P6 Canada ..."
Abstract

Cited by 29 (19 self)
 Add to MetaCart
March 1, 2002 Rodney G. Downey Department of Mathematics, Victoria University P.O. Box 600, Wellington, New Zealand downey@math.vuw.ac.nz Michael R. Fellows, Bruce M. Kapron and Michael T. Hallett Department of Computer Science, University of Victoria Victoria, British Columbia V8W 3P6 Canada contact author: mfellows@csr.uvic.ca H. Todd Wareham Department of Computer Science Memorial University of Newfoundland St. Johns, Newfoundland A1C 5S7 Canada harold@odie.cs.mun.ca Summary The theory of parameterized computational complexity introduced in [DF13] appears to be of wide applicability in the study of the complexity of concrete problems [ADF,BFH,DEF,FHW,FK]. We believe the theory may be of particular importance to practical applications of logic formalisms in programming language design and in system specification. The reason for this relevance is that while many computational problems in logic are extremely intractable generally, realistic applications often involve a "hidden parameter" according to which the computational problem may be feasible according to the more sensitive criteria of fixedparameter tractability that is the central issue in parameterized computational complexity. We illustrate how this theory may apply to problems in logic, programming languages and linguistics by describing some examples of both tractability and intractability results in these areas. It is our strong expectation that these results are just the tip of the iceberg of interesting applications of parameterized complexity theory to logic and linguistics. The main results described in this abstract are as follows. (1) The problem of determining whether a word x can be derived in k steps in a contextsensitive grammar G (Short CSL Derivation) is complete for the paramet...
Improved algorithms for the feedback vertex set problems
, 2007
"... We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5 k kn 2). For unweighted graphs, our algorithm either constructs a feedback vertex set of size bounded by k in a given graph G, or reports that no s ..."
Abstract

Cited by 27 (7 self)
 Add to MetaCart
We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5 k kn 2). For unweighted graphs, our algorithm either constructs a feedback vertex set of size bounded by k in a given graph G, or reports that no such a feedback vertex set exists in G. For weighted graphs, our algorithm either constructs a minimumweight feedback vertex set of size bounded by k in a given graph G, or reports that no feedback vertex set of size bounded by k exists in G.
M.R.: Parameterized learning complexity
 In: Proc. 6th Annual ACM Conference on Computational Learning Theory
, 1993
"... We describe three applications in computational learning theory of techniques and ideas recently introduced in the study of parameterized computational complexity. (1) Using parameterized problem reducibilities, we show that Psized DNF (CNF) formulas can be exactly learned in time polynomial in the ..."
Abstract

Cited by 17 (11 self)
 Add to MetaCart
We describe three applications in computational learning theory of techniques and ideas recently introduced in the study of parameterized computational complexity. (1) Using parameterized problem reducibilities, we show that Psized DNF (CNF) formulas can be exactly learned in time polynomial in the number of variables by extended equivalence queries if and only if the dominating sets of a graph can be learned in polynomial time by extended equivalence queries. (That is, learning by an arbitary hypothesis class. See Angluin [?].) Since learning dominating sets is a special case of learning monotone CNF formulas, this extends to the exact learning model a result of Kearns, li, Pitt and Valiant in the PAC prediction model [?]. We show that Psized DNF (CNF) formulas can be learned exactly in polynomial time by extended equivalence and membership queries if and only there is an algorithm running in time polynomial in n and k to learn the k element dominating sets of an n vertex graph. We also prove related results concerning the problem of learning the truth assignments of weight k for DNF (CNF) formulas (that is, assignments that set exactly k variables to true and the rest to false). (2) We describe a number of learning algorithms for both parameterized and unparameterized graphtheoretic learning problems, such as learning the independent sets, vertex covers or dominating sets of a graph. (3) We show that computing the VapnikChervonenkis dimension of a family of sets is complete for the parameterized complexity class W [1]. 1.
FixedParameter Complexity in AI and Nonmonotonic Reasoning
, 1999
"... This paper studies the fixedparameter complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixedparameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
This paper studies the fixedparameter complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixedparameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed domain, restricted satisfiability problems, propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the program's dependency graph, and circumscriptive inference from a positive kCNF restricted to models of bounded size. We also show that circumscriptive inference from a general propositional theory, when the attention is restricted to models of bounded size, is fixedparameter intractable and is actually complete for a novel fixedparameter complexity class. Keywords: Complexity, Fixedparameter Tractability, Nonmonotonic Reasoning, Constraint Satisfaction, Prime Implicants, Logic Programming, Stable Models, C...
LinearTime Register Allocation for a Fixed Number of Registers
 PROCEEDINGS SODA’98
, 1998
"... We show that for any fixed number of registers there is a lineartime algorithm which given a structured (j gotofree) program finds, if possible, an allocation of variables to registers without using intermediate storage. Our algorithm allows for rescheduling, i.e. that straightline sequences of ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
We show that for any fixed number of registers there is a lineartime algorithm which given a structured (j gotofree) program finds, if possible, an allocation of variables to registers without using intermediate storage. Our algorithm allows for rescheduling, i.e. that straightline sequences of statements may be reordered to achieve a better register allocation as long as the data dependencies of the program are not violated. If we also allow for registers of different types, e.g. for integers and floats, we can give only a polynomial time algorithm. In fact we show that the problem then becomes hard for the Whierarchy which is a strong indication that no O(n c ) algorithm exists for it with c independent on the number of registers. However, if we do not allow for rescheduling then this nonuniform register case is also solved in linear time.
FPTalgorithms for connected feedback vertex set
, 2009
"... We study the recently introduced CONNECTED FEEDBACK VERTEX SET (CFVS) problem from the viewpoint of parameterized algorithms. CFVS is the connected variant of the classical FEEDBACK VERTEX SET problem and is defined as follows: given a graph G = (V, E) and an integer k, decide whether there exists ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We study the recently introduced CONNECTED FEEDBACK VERTEX SET (CFVS) problem from the viewpoint of parameterized algorithms. CFVS is the connected variant of the classical FEEDBACK VERTEX SET problem and is defined as follows: given a graph G = (V, E) and an integer k, decide whether there exists F ⊆ V, F  ≤ k, such that G[V \ F] is a forest and G[F] is connected. We show that CONNECTED FEEDBACK VERTEX SET can be solved in time O(2 O(k) n O(1)) on general graphs and in time O(2 O( √ k log k) n O(1)) on graphs excluding a fixed graph H as a minor. Our result on general undirected graphs uses, as a subroutine, a parameterized algorithm for GROUP STEINER TREE, a well studied variant of STEINER TREE. We find the algorithm for GROUP STEINER TREE of independent interest and believe that it could be useful for obtaining parameterized algorithms for other connectivity problems.
On the Parameterized MaxLeaf Problems: Digraphs and Undirected Graphs ∗
"... The parameterized maxleaf problem on undirected graphs (which is also named the maxleaf spanningtree problem) is formulated as follows: given an undirected graph G and a parameter k, either construct a spanning tree with at least k leaves for G or report ‘No ’ if such a tree does not exist. The p ..."
Abstract
 Add to MetaCart
The parameterized maxleaf problem on undirected graphs (which is also named the maxleaf spanningtree problem) is formulated as follows: given an undirected graph G and a parameter k, either construct a spanning tree with at least k leaves for G or report ‘No ’ if such a tree does not exist. The problem also has a version for directed graphs that is named the maxleaf outbranching problem. In this paper, we present a simple branchandsearch algorithm of running time O ∗ (4 k) that solves the maxleaf outbranching problem. This significantly improves the previous best algorithm for the problem that runs in time O ∗ (2 O(k log k)). Our main contributions consist of new observations on the combinatorial structures of the problem and the introduction of a new algorithmic technique that provides new perspectives for design and analysis of parameterized algorithms. Our algorithm of running time O ∗ (4 k) is also applicable to the simpler maxleaf spanningtree problem, improving the previous best algorithm of running time O ∗ (6.75 k) for the problem. 1