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213
Acyclic Subgraphs of Planar Digraphs
, 2014
"... An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on n vertices without directed 2cycles possesses an acyclic set of size at least 3n/5. We prove this conjecture for digraphs where every directed cycle has l ..."
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Cited by 1 (0 self)
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An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on n vertices without directed 2cycles possesses an acyclic set of size at least 3n/5. We prove this conjecture for digraphs where every directed cycle has
Approximations For The Maximum Acyclic Subgraph Problem
 Information Processing Letters
, 1994
"... : Given a directed graph G = (V; A), the maximum acyclic subgraph problem is to compute a subset, A 0 , of arcs of maximum size or total weight so that G 0 = (V; A 0 ) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(jAj + d 3 max ) algorithm ..."
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Cited by 18 (1 self)
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: Given a directed graph G = (V; A), the maximum acyclic subgraph problem is to compute a subset, A 0 , of arcs of maximum size or total weight so that G 0 = (V; A 0 ) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(jAj + d 3 max ) algorithm
On the Advantage over Random for Maximum Acyclic Subgraph
"... In this paper we present a new approximation algorithm for the MAX ACYCLIC SUBGRAPH problem. Given an instance where the maximum acyclic subgraph contains 1/2+δ fraction of all edges, our algorithm finds an acyclic subgraph with 1/2 + Ω(δ / logn) fraction of all edges. 1 ..."
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Cited by 13 (5 self)
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In this paper we present a new approximation algorithm for the MAX ACYCLIC SUBGRAPH problem. Given an instance where the maximum acyclic subgraph contains 1/2+δ fraction of all edges, our algorithm finds an acyclic subgraph with 1/2 + Ω(δ / logn) fraction of all edges. 1
ACYCLIC SUBGRAPHS IN kMAJORITY TOURNAMENTS
"... Abstract. A kmajority digraph is a directed graph created by combining k individual rankings on the same ground set to form a consensus where edges point in the direction indicated by a strict majority of the rankings. The kmajority digraph is used to model voting scenarios, where the vertices cor ..."
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Abstract. A kmajority digraph is a directed graph created by combining k individual rankings on the same ground set to form a consensus where edges point in the direction indicated by a strict majority of the rankings. The kmajority digraph is used to model voting scenarios, where the vertices correspond to options ranked by k voters. When k is odd, the resulting digraph is always a tournament, called kmajority tournament. Let fk(n) be the minimum, over all kmajority tournaments with n vertices, of the maximum order of an induced transitive subtournament. Recently, Milans, Schreiber, and West proved that n ≤ f3(n) ≤ 2√n+1. In this paper, we improve the upper bound of f3(n) by showing that f3(n) <
The Strongest Facets of the Acyclic Subgraph Polytope are Unknown
 INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, LECTURES NOTES IN COMPUTER SCIENCE 1084
, 1996
"... We consider the acyclic subgraph polytope and define the notion of strength of a relaxation as the maximum improvement obtained by using this relaxation instead of the most trivial relaxation of the problem. We show that the strength of a relaxation is the maximum of the strengths of the relaxation ..."
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Cited by 18 (0 self)
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We consider the acyclic subgraph polytope and define the notion of strength of a relaxation as the maximum improvement obtained by using this relaxation instead of the most trivial relaxation of the problem. We show that the strength of a relaxation is the maximum of the strengths
Finding Induced Acyclic Subgraphs in Random Digraphs
, 2003
"... Consider the problem of finding a large induced acyclic subgraph of a given simple digraph D =(V,E). The decision version of this problem is NPcomplete and its optimization is not likely to be approximable within a ratio of O(n )for some #>0. We study this problem when D is a random instance. ..."
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Cited by 2 (1 self)
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Consider the problem of finding a large induced acyclic subgraph of a given simple digraph D =(V,E). The decision version of this problem is NPcomplete and its optimization is not likely to be approximable within a ratio of O(n )for some #>0. We study this problem when D is a random instance
Beating the random ordering is hard: Inapproximability of maximum acyclic subgraph
 in FOCS, 2008
"... We prove that approximating the Max Acyclic Subgraph problem within a factor better than 1/2 is UniqueGames hard. Specifically, for every constant ε> 0 the following holds: given a directed graph G that has an acyclic subgraph consisting of a fraction (1 − ε) of its edges, if one can efficiently ..."
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Cited by 36 (9 self)
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We prove that approximating the Max Acyclic Subgraph problem within a factor better than 1/2 is UniqueGames hard. Specifically, for every constant ε> 0 the following holds: given a directed graph G that has an acyclic subgraph consisting of a fraction (1 − ε) of its edges, if one can
Induced acyclic subgraphs in random digraphs: Improved bounds
"... Given a simple directed graph D = (V, A), let the size of the largest induced directed acyclic graph (dag) be denoted by mas(D). Let D ∈ D(n, p) be a random instance, obtained by choosing each of the () n possible undirected 2 edges independently with probability 2p and then orienting each chosen ed ..."
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Given a simple directed graph D = (V, A), let the size of the largest induced directed acyclic graph (dag) be denoted by mas(D). Let D ∈ D(n, p) be a random instance, obtained by choosing each of the () n possible undirected 2 edges independently with probability 2p and then orienting each chosen
Results 1  10
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213