Efficient algorithms for the 2-gathering problem

Alon Shalita; Uri Zwick

doi:10.1137/1.9781611973068.11

Efficient algorithms for the 2-gathering problem

Alon Shalita^*, Uri Zwick

^*Corresponding author for this work

School of Computer Science

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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.

Original language	English
Title of host publication	Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher	Association for Computing Machinery (ACM)
Pages	96-105
Number of pages	10
ISBN (Print)	9780898716801
DOIs	https://doi.org/10.1137/1.9781611973068.11
State	Published - 2009
Event	20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States Duration: 4 Jan 2009 → 6 Jan 2009

Publication series

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

Conference

Conference	20th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/Territory	United States
City	New York, NY
Period	4/01/09 → 6/01/09

Access to Document

10.1137/1.9781611973068.11

Cite this

@inproceedings{4e4bc7a7d85042e9829eaff6b4f97bd8,

title = "Efficient algorithms for the 2-gathering problem",

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.",

author = "Alon Shalita and Uri Zwick",

year = "2009",

doi = "10.1137/1.9781611973068.11",

language = "אנגלית",

isbn = "9780898716801",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery (ACM)",

pages = "96--105",

booktitle = "Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms",

address = "ארצות הברית",

note = "20th Annual ACM-SIAM Symposium on Discrete Algorithms ; Conference date: 04-01-2009 Through 06-01-2009",

}

Shalita, A & Zwick, U 2009, Efficient algorithms for the 2-gathering problem. in Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery (ACM), pp. 96-105, 20th Annual ACM-SIAM Symposium on Discrete Algorithms, New York, NY, United States, 4/01/09. https://doi.org/10.1137/1.9781611973068.11

Efficient algorithms for the 2-gathering problem. / Shalita, Alon; Zwick, Uri.
Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms. Association for Computing Machinery (ACM), 2009. p. 96-105 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

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 -

Efficient algorithms for the 2-gathering problem

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this