A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Minimum Cycle Bases for Network Graphs
Algorithmica
Meshing genus-1 point clouds using discrete one-forms
Computers and Graphics
Algorithms to Compute Minimum Cycle Basis in Directed Graphs
Theory of Computing Systems
A greedy approach to compute a minimum cycle basis of a directed graph
Information Processing Letters
An Õ(m2n) randomized algorithm to compute a minimum cycle basis of a directed graph
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A faster deterministic algorithm for minimum cycle bases in directed graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Implementing minimum cycle basis algorithms
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Cycle bases of graphs and sampled manifolds
Computer Aided Geometric Design
Efficient approximation algorithms for shortest cycles in undirected graphs
Information Processing Letters
Minimum Cycle Bases and Their Applications
Algorithmics of Large and Complex Networks
Minimum cycle bases: Faster and simpler
ACM Transactions on Algorithms (TALG)
Minimum Cycle Bases of Weighted Outerplanar Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Efficient approximation algorithms for shortest cycles in undirected graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Minimum cycle bases of weighted outerplanar graphs
Information Processing Letters
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Minimum cycle bases in graphs algorithms and applications
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Hi-index | 0.01 |
We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0, 1} incidence vector is associated with each cycle and the vector space over F2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k ≥ 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn1+2/k + mn(1+1/k)(ω-1)) and deterministic running time O(n3+2/k), respectively. Here ω is the best exponent of matrix multiplication. It is presently known that ω o(mω) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Θ(mω) bound. We also present a 2-approximation algorithm with O(mω√nlogn) expected running time, a linear time 2-approximation algorithm for planar graphs and an O(n3) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.