TY - JOUR

T1 - Efficient algorithms for the 2-gathering problem

AU - Shalita, Alon

AU - Zwick, Uri

PY - 2010/3/1

Y1 - 2010/3/1

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 nontrivial generalization of the nonbipartite 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 nontrivial generalization of the nonbipartite matching problem and it is solved by extending the augmenting paths technique used to solve matching problems.

KW - 2-gatherings

KW - Augmenting paths

KW - Nonbipartite matchings

UR - http://www.scopus.com/inward/record.url?scp=77950817533&partnerID=8YFLogxK

U2 - 10.1145/1721837.1721850

DO - 10.1145/1721837.1721850

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AN - SCOPUS:77950817533

SN - 1549-6325

VL - 6

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 2

M1 - 34

ER -