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Journal of the ACM (JACM)
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Journal of Symbolic Computation - Special issue on computational algebraic complexity
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SIAM Journal on Computing
Journal of the ACM (JACM)
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
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SIAM Journal on Computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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Faster algorithms for finding lowest common ancestors in directed acyclic graphs
Theoretical Computer Science
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SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
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Information Processing Letters
General context-free recognition in less than cubic time
Journal of Computer and System Sciences
Regularity Lemmas and Combinatorial Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Minimum Weight Cycles and Triangles: Equivalences and Algorithms
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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We study the problem of determining the girth of an unweighted undirected graph. We obtain several new efficient approximation algorithms for graphs with n nodes and m edges and unknown girth g. We consider additive and multiplicative approximations. Additive Approximations. We present: • an Õ(n3/m)-time algorithm which returns a cycle of length at most g + 2 if g is even and g + 3 if g is odd. This complements the seminal work of Itai and Rodeh [SIAM J. Computing'78] who gave an algorithm that in O(n2) time finds a cycle of length g if g is even, and g + 1 if g is odd. • an Õ(n3/m)-time algorithm which returns a cycle of length at most g' + 2 if g' is the length of the shortest even cycle in G. This result complements the work of Yuster and Zwick [SIAM J. Discrete Math'97] who showed how to compute g' in O(n2) time. Multiplicative Approximations. We present: • an Õ(n5/3)-time algorithm which returns a cycle of length at most 3g/2 + z/2 when g is even and 3g/2 + z/2 + 1 when g is odd, where z = −g mod 4, z ε {0, 1, 2, 3}. This gives an Õ(n5/3)-time 2-approximation for the girth, the first subquadratic 2-approximation algorithm, resolving an open question of Lingas and Lundell [IPL'09]. • an O(n1.968)-time (8/5)-approximation algorithm for the girth in graphs with girth at least 4 (i.e., triangle-free graphs). This is the first subquadratic time (2 -- ε)-approximation algorithm for the girth for triangle-free graphs, for any ε 0. We prove that a deterministic algorithm of this kind is not possible for directed graphs, thus showing a strong separation between undirected and directed graphs for girth approximation.