Efficient algorithms for the 2-gathering problem

Authors:
Alon Shalita;Uri Zwick
Affiliations:
Tel Aviv University, Tel Aviv, Israel;Tel Aviv University, Tel Aviv, Israel
Venue:
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Year:
2009

Citing 9
Cited 1

General factors of graphs

Journal of Combinatorial Theory Series B
Faster scaling algorithms for general graph matching problems

Journal of the ACM (JACM)
General antifactors of graphs

Journal of Combinatorial Theory Series B
Clique partitions, graph compression and speeding-up algorithms

Journal of Computer and System Sciences
An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Terminal backup, 3D matching, and covering cubic graphs

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Aspects of network design

Aspects of network design
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs

SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
On min-max r-gatherings

WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms

Terminal Backup, 3D Matching, and Covering Cubic Graphs

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Pebbles are placed on some vertices of a directed graph. Is it possible to move each pebble along at most one edge of the graph so that in the final configuration no pebble is left on its own? We give an O(mn)-time algorithm for solving this problem, which we call the 2-gathering problem, where n is the number of vertices and m is the number of edges of the graph. If such a 2-gathering is not possible, the algorithm finds a solution that minimizes the number of solitary pebbles. The 2-gathering problem forms a non-trivial generalization of the non-bipartite matching problem and it is solved by extending the augmenting paths technique used to solve matching problems.