TY - GEN

T1 - Efficient algorithms for the 2-gathering problem

AU - Shalita, Alon

AU - Zwick, Uri

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70349133935&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973068.11

DO - 10.1137/1.9781611973068.11

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AN - SCOPUS:70349133935

SN - 9780898716801

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 96

EP - 105

BT - Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Association for Computing Machinery (ACM)

T2 - 20th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 4 January 2009 through 6 January 2009

ER -