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From Small Space to Small Width in Resolution
"... In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of formulas is always an upper bound on the width needed to refute them. Their proof is beautiful but somewhat mysterious in that it relies heavily on tools from fi ..."
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In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of formulas is always an upper bound on the width needed to refute them. Their proof is beautiful but somewhat mysterious in that it relies heavily on tools from
An Improved Algorithm For Finding Tree Decompositions Of Small Width
, 2000
"... We present a modification of Bodlaender's linear time algorithm that, for constant k, determines whether an input graph G has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k th ..."
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Cited by 19 (4 self)
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We present a modification of Bodlaender's linear time algorithm that, for constant k, determines whether an input graph G has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k
Testing of Function that have small width Branching Programs
 Proc. of 41 th FOCS
, 2000
"... Combinatorial property testing, initiated formally by Goldreich, Goldwasser and Ron in [11], and inspired by Rubinfeld and Sudan [13], deals with the following relaxation of decision problems: Given a fixed property and an input x, one wants to decide whether x has the property or is being 'far ..."
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Cited by 20 (6 self)
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;far' from having the property. The main result here is that if G = fg : f0; 1g n ! f0; 1gg is a family of Boolean functions that have readonce branching programs of width w, then for every n and > 0 there is a randomized algorithm that always accepts every x 2 f0; 1g n if g(x) = 1, and rejects
Lower Bounds for WidthRestricted Clause Learning on Formulas of Small Width
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... Clause learning is a technique used by backtrackingbased propositional satisfiability solvers, where some clauses obtained by analysis of conflicts are added to the formula during backtracking. It has been observed empirically that clause learning does not significantly improve the performance of a ..."
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Cited by 7 (1 self)
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of a solver when restricted to learning clauses of small width only. This experience is supported by lower bound theorems. It is shown that lower bounds on the runtime of widthrestricted clause learning follow from lower bounds on the width of resolution proofs. This yields the first lower bounds
The Fixed Point Property For Posets Of Small Width
, 1998
"... . The fixed point property for finite posets of width 3 and 4 is studied in terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4 are determined explicitly. The ranked forbidden retracts for the width 3 case that are linearly indecomposable are examined to see which are minima ..."
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Cited by 2 (0 self)
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. The fixed point property for finite posets of width 3 and 4 is studied in terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4 are determined explicitly. The ranked forbidden retracts for the width 3 case that are linearly indecomposable are examined to see which
Lower bounds for testing computability by small width OBDDs
 IN PROC. 8TH ANNUAL THEORY AND APPLICATIONS OF MODELS OF COMPUTATION
, 2011
"... We consider the problem of testing whether a function f: {0, 1} n → {0, 1} is computable by a readonce, width2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where the v ..."
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Cited by 5 (1 self)
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We consider the problem of testing whether a function f: {0, 1} n → {0, 1} is computable by a readonce, width2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where
Recognition Algorithms for Orders of Small Width and Graphs of Small Dilworth Number
"... Partially ordered sets of small width and graphs of small Dilworth number have many interesting properties and have been well studied. Here we show that recognition of such orders and graphs can be done more eÆciently than by using the wellknown algorithms based on bipartite matching and matrix mul ..."
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Cited by 14 (0 self)
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Partially ordered sets of small width and graphs of small Dilworth number have many interesting properties and have been well studied. Here we show that recognition of such orders and graphs can be done more eÆciently than by using the wellknown algorithms based on bipartite matching and matrix
Testing membership in languages that have small width branching programs
 SIAM Journal on Computing
"... Abstract. Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and ..."
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Cited by 22 (5 self)
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Abstract. Combinatorial property testing, initiated formally by Goldreich, Goldwasser, and
A Simple LinearTime Algorithm for Finding PathDecompositions of Small Width
 also University of Victoria manuscript
, 1996
"... We described a simple algorithm running in linear time for each fixed constant k, that either establishes that the pathwidth of a graph G is greater than k, or finds a pathdecomposition of G of width at most O(2^k). This provides a simple proof of the result by Bodlaender that many families of grap ..."
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Cited by 3 (2 self)
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We described a simple algorithm running in linear time for each fixed constant k, that either establishes that the pathwidth of a graph G is greater than k, or finds a pathdecomposition of G of width at most O(2^k). This provides a simple proof of the result by Bodlaender that many families
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