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Results 1 - 10
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21,212
Exponential-time approximation of weighted set cover
- Inf. Process. Lett
"... The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parame-ter tractable, under widely believed complexity assumptions. In recent years, many re-searchers design exact exponential-time algorithms for ..."
Abstract
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Cited by 9 (0 self)
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The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parame-ter tractable, under widely believed complexity assumptions. In recent years, many re-searchers design exact exponential-time algorithms
An Improved Exponential-time Algorithm for k-SAT
, 1998
"... We propose and analyze a simple new randomized algorithm, called ResolveSat, for finding satisfying assignments of Boolean formulas in conjunctive normal form. The algorithm consists of two stages: a preprocessing stage in which resolution is applied to enlarge the set of clauses of the formula, ..."
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Cited by 111 (7 self)
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satisfying assignment of a general satisfiable 3--CNF in time O(2 :448n ) with high probability; where the best previous algorithm [13] has running time O(2 :562n ). We obtain a better upper bound of 2 (2 ln 2\Gamma1)n+o(n) = O(2 0:387n ) for 3CNF that have exactly one satisfying assignment
Exact exponential-time algorithms for finding bicliques
, 2010
"... Due to a large number of applications, bicliques of graphs have been widely considered in the literature. This paper focuses on non-induced bicliques. Given a graph G = (V, E) on n vertices, a pair (X, Y), with X, Y ⊆ V, X ∩ Y = ∅, is a non-induced biclique if {x, y} ∈ E for any x ∈ X and y ∈ Y. Th ..."
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Cited by 3 (0 self)
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. The NP-complete problem of finding a non-induced (k1, k2)-biclique asks to decide whether G contains a non-induced biclique (X, Y) such that |X | = k1 and |Y | = k2. In this paper, we design a polynomial-space O(1.6914 n)-time algorithm for this problem. It is based on an algorithm for bipartite graphs
Hardness results and an Exact Exponential Algorithm for the . . .
, 2011
"... Spanning tree congestion is a relatively new graph parameter, which has been studied intensively. This paper studies the complexity of the problem to determine the spanning tree congestion for non-sparse graph classes, while it was investigated for some sparse graph classes before. We prove that the ..."
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Cited by 1 (1 self)
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that the problem is NP-hard even for chain graphs and split graphs. To cope with the hardness of the problem, we present a fast (exponential-time) exact algorithm that runs in O ∗ (2 n) time, where n denotes the number of vertices. Additionally, we present simple combinatorial lemmas, which yield a constant
The Quickhull algorithm for convex hulls
- ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 713 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental
Factor Graphs and the Sum-Product Algorithm
- IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
Abstract
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Cited by 1791 (69 self)
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computational rule, the sum-product algorithm operates in factor graphs to compute---either exactly or approximately---various marginal functions by distributed message-passing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
Graph-based algorithms for Boolean function manipulation
- IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3526 (46 self)
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on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (9 self)
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This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time compl ..."
Abstract
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Cited by 1315 (53 self)
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After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time
Results 1 - 10
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21,212
