Article

I/O-optimal algorithms for planar graphs using separators

Authors:

Anil Maheshwari,

Norbert ZehAuthors Info & Claims

SODA '02: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms

Pages 372 - 381

Published: 06 January 2002 Publication History

Abstract

We present I/O-optimal algorithms for several fundamental problems on planar graphs. Our main contribution is an I/O-efficient algorithm for computing a small vertex separator of an unweighted planar graph. This algorithm is superior to all existing external memory algorithms for this problem, as it requires neither a breadth-first search tree nor an embedding of the graph as part of the input. In fact, we derive I/O-optimal algorithms for planar embedding, breadth-first search, depth-first search, single source shortest paths, and computing weighted separators of planar graphs from our unweighted separator algorithm.

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Cited By

Arge Lvan Walderveen FZeh NKhanna S(2013)Multiway simple cycle separators and I/O-efficient algorithms for planar graphsProceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms10.5555/2627817.2627882(901-918)Online publication date: 6-Jan-2013
https://dl.acm.org/doi/10.5555/2627817.2627882
Vitter J(2008)Algorithms and data structures for external memoryFoundations and Trends® in Theoretical Computer Science10.1561/04000000142:4(305-474)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.1561/0400000014
Hazel TToma LVahrenhold JWickremesinghe R(2008)TerracostACM Journal of Experimental Algorithmics10.1145/1227161.137060012(1-31)Online publication date: 12-Jun-2008
https://dl.acm.org/doi/10.1145/1227161.1370600
Show More Cited By

I/O-optimal algorithms for planar graphs using separators
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation

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Published In

cover image ACM Conferences

SODA '02: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms

January 2002

1018 pages

ISBN:089871513X

Conference Chair:
David Eppstein

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 06 January 2002

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Arge Lvan Walderveen FZeh NKhanna S(2013)Multiway simple cycle separators and I/O-efficient algorithms for planar graphsProceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms10.5555/2627817.2627882(901-918)Online publication date: 6-Jan-2013
https://dl.acm.org/doi/10.5555/2627817.2627882
Vitter J(2008)Algorithms and data structures for external memoryFoundations and Trends® in Theoretical Computer Science10.1561/04000000142:4(305-474)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.1561/0400000014
Hazel TToma LVahrenhold JWickremesinghe R(2008)TerracostACM Journal of Experimental Algorithmics10.1145/1227161.137060012(1-31)Online publication date: 12-Jun-2008
https://dl.acm.org/doi/10.1145/1227161.1370600
Ajwani DDementiev RMeyer U(2006)A computational study of external-memory BFS algorithmsProceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm10.5555/1109557.1109623(601-610)Online publication date: 22-Jan-2006
https://dl.acm.org/doi/10.5555/1109557.1109623
Haverkort HToma L(2006)I/O-Efficient algorithms on near-planar graphsProceedings of the 7th Latin American conference on Theoretical Informatics10.1007/11682462_54(580-591)Online publication date: 20-Mar-2006
https://dl.acm.org/doi/10.1007/11682462_54
Her JRamakrishna R(2005)External-memory depth-first search algorithm for solid grid graphsInformation Processing Letters10.5555/1062041.171102493:4(177-183)Online publication date: 28-Feb-2005
https://dl.acm.org/doi/10.5555/1062041.1711024
Arge LToma L(2005)External data structures for shortest path queries on planar digraphsProceedings of the 16th international conference on Algorithms and Computation10.1007/11602613_34(328-338)Online publication date: 19-Dec-2005
https://dl.acm.org/doi/10.1007/11602613_34
Jampala HZeh N(2005)Cache-oblivious planar shortest pathsProceedings of the 32nd international conference on Automata, Languages and Programming10.1007/11523468_46(563-575)Online publication date: 11-Jul-2005
https://dl.acm.org/doi/10.1007/11523468_46
Arge LToma LZeh NRosenberg AMeyer auf der Heide F(2003)I/O-efficient topological sorting of planar DAGsProceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures10.1145/777412.777427(85-93)Online publication date: 7-Jun-2003
https://dl.acm.org/doi/10.1145/777412.777427
Sibeyn JAbello JMeyer URosenberg AMaggs B(2002)Heuristics for semi-external depth first search on directed graphsProceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures10.1145/564870.564917(282-292)Online publication date: 10-Aug-2002
https://dl.acm.org/doi/10.1145/564870.564917

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