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A deterministic subexponential algorithm for solving parity games
 SODA
, 2006
"... The existence of polynomial time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. These algorithms are all ultimately based on the randomized subexponential simplex algorithms ..."
Abstract

Cited by 82 (3 self)
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The existence of polynomial time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. These algorithms are all ultimately based on the randomized subexponential simplex algorithms
Subexponential Algorithms for Partial Cover Problems
"... Partial Cover problems are optimization versions of fundamental and well studied problems like Vertex Cover and Dominating Set. Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number (k) of vertices, rather than covering all edges (or vertic ..."
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Cited by 9 (3 self)
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graphs, which include planar graphs and graphs of bounded genus. In particular, it was shown that on planar graphs both problems can be solved in time 2 O(k) n O(1). During the last decade there has been an extensive study on parameterized subexponential algorithms. In particular, it was shown
Randomized Subexponential Algorithms for Infinite Games
, 2004
"... The complexity of solving infinite games, including parity, mean payoff, and simple stochastic games, is an important open problem in verification, automata theory, and complexity theory. In this paper we develop an abstract setting for studying and solving such games, as well as related problems, b ..."
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Cited by 6 (0 self)
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relation to the previously wellstudied completely unimodal (CU) and localglobal functions. A number of nice properties of CLGfunctions are proved. In this setting, we survey several randomized optimization algorithms appropriate for CU, CLG, and RLGfunctions. We show that the subexponential
Subexponential algorithms for Unique Games and related problems
 IN 51 ST IEEE FOCS
, 2010
"... We give subexponential time approximation algorithms for the unique games and the small set expansion problems. Specifically, for some absolute constant c, we give: 1. An exp(kn ε)time algorithm that, given as input a kalphabet unique game on n variables that has an assignment satisfying 1 − ε c f ..."
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Cited by 82 (7 self)
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We give subexponential time approximation algorithms for the unique games and the small set expansion problems. Specifically, for some absolute constant c, we give: 1. An exp(kn ε)time algorithm that, given as input a kalphabet unique game on n variables that has an assignment satisfying 1 − ε c
Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs
"... In 2000 Alber et al. [SWAT 2000] obtained the first parameterized subexponential algorithm on undirected planar graphs by showing that kDOMINATING SET is solvable in time 2 O( √ k) ..."
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Cited by 7 (6 self)
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In 2000 Alber et al. [SWAT 2000] obtained the first parameterized subexponential algorithm on undirected planar graphs by showing that kDOMINATING SET is solvable in time 2 O( √ k)
Designing Subexponential Algorithms: Problems, Techniques & Structures
, 2007
"... In this thesis we focus on subexponential algorithms for NPhard graph problems: exact and parameterized algorithms that have a truly subexponential running time behavior. For input instances of size n we study exact algorithms with running time 2 O( √ n) and parameterized algorithms with running ti ..."
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Cited by 4 (0 self)
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In this thesis we focus on subexponential algorithms for NPhard graph problems: exact and parameterized algorithms that have a truly subexponential running time behavior. For input instances of size n we study exact algorithms with running time 2 O( √ n) and parameterized algorithms with running
Subexponential algorithm for unique games Claire Mathieu
, 2011
"... A summary of the AroraBarakSteurer 2010 subexponential algorithm for unique games – without proofs. 1 Problem and result Here is the unique games problem. Fix an integer p> 0. Input: A multigraph G, each edge being labeled by an equation. Edge {i, j} is labeled by an equation of the form: xi − ..."
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A summary of the AroraBarakSteurer 2010 subexponential algorithm for unique games – without proofs. 1 Problem and result Here is the unique games problem. Fix an integer p> 0. Input: A multigraph G, each edge being labeled by an equation. Edge {i, j} is labeled by an equation of the form: xi
A subexponential algorithm for abstract optimization problems
 SIAM J. Comput
, 1995
"... An Abstract Optimization Problem (AOP) is a triple (H, <, Φ) where H is a finite set, < a total order on 2 H and Φ an oracle that, for given F ⊆ G ⊆ H, either reports that F = min<{F ′  F ′ ⊆ G} or returns a set F ′ ⊆ G with F ′ < F. To solve the problem means to find the minimum set ..."
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Cited by 48 (4 self)
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set in H. We present a randomized algorithm that solves any AOP with an expected number of at most e 2 √ n+O ( 4 √ n ln n) oracle calls, n = H. In contrast, any deterministic algorithm needs to make 2 n − 1 oracle calls in the worst case. The algorithm is applied to the problem of finding
Results 1  10
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6,821