A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
Introduction to algorithms
Journal of the ACM (JACM)
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
Finding Even Cycles Even Faster
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Packing cycles in undirected graphs
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Finding a maximum weight triangle in n3-Δ time, with applications
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Finding a heaviest triangle is not harder than matrix multiplication
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
New approximation algorithms for minimum cycle bases of graphs
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Disjoint cycles: integrality gap, hardness, and approximation
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Finding the smallest H-Subgraph in real weighted graphs and related problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
All-pairs nearly 2-approximate shortest-paths in O(n2 polylog n) time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Finding, counting and listing all triangles in large graphs, an experimental study
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Computing the girth of a planar graph in linear time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Subquadratic time approximation algorithms for the girth
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
ACM Transactions on Algorithms (TALG)
A comparative study of parallel algorithms for the girth problem
AusPDC '12 Proceedings of the Tenth Australasian Symposium on Parallel and Distributed Computing - Volume 127
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We describe a simple combinatorial approximation algorithm for finding a shortest (simple) cycle in an undirected graph. Given an adjacency-list representation of an undirected graph G with n vertices and unknown girth k, our algorithm returns with high probability a cycle of length at most 2k for even k and 2k+2 for odd k, in time O(n^3^2logn). Thus, in general, it yields a 223 approximation. For a weighted, undirected graph, with non-negative edge weights in the range {1,2,...,M}, we present a simple combinatorial 2-approximation algorithm for a minimum weight (simple) cycle that runs in time O(n^2logn(logn+logM)).