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Forests, frames, and games: algorithms for matroid sums and applications

Authors:

Herbert WestermannAuthors Info & Claims

STOC '88: Proceedings of the twentieth annual ACM symposium on Theory of computing

Pages 407 - 421

https://doi.org/10.1145/62212.62252

Published: 01 January 1988 Publication History

Abstract

This paper presents improved algorithms for matroid partitioning problems, such as finding a maximum cardinality set of edges of a graph that can be partitioned into k forests. The notion of a clamp in a matroid sum is introduced. Efficient algorithms for problems involving clumps are presented. Applications of these algorithms to problems arising in the study of structural rigidity of graphs, the Shannon switching game and others are given.

References

[1]

M. Aigner, ('ombinotorial Theory, Spriage,'-Vorlag, New York, 197,{).

[2]

John Bruno, ",\lat. roitls graphs and r('si.,tance networks", Ph.D. {lis.sertation, I)ept. Elee. Eng., City College of New York, New York. l:)67.

[3]

J. Bruno and L. Weinberg, "A constructive graph-lheoretic solution of l llo ~haltnoll s~,'itching ganle", IEEE Trans. Curcuit theory ( T-17, 1, 1970,pp. 74-81.

[4]

J. Bruno and L. Weinberg, "Tile prilicipal lttinors,ff a inatroi(l", Linear algebra and Its Apphcations,l. 1971. pp. t7- 5.1.

[5]

N. Chiba and T. Nishizeki", Arhoricity and subgraph listing algori~hms", SIAM J. Comput. 14, 1, 1085, pp. 210-223.

Digital Library

[6]

E.A. Dinic, "Algorithm for solution of a problem of maximum flow in a network with power estimat ion", Nor. Math. Dokl. It,5, 1970. pp. t277-1280.

[7]

J. Edmonds, "Miaimum partition of a matroid into ind,-- pendent subsets". J. Res. National Bureau of Standards 6911, 196,5, pp. 67-72.

[8]

J. Edmonds, "Lehmau's switching same and a theorem of Tutte, and Nash-Williams". d. tte.~. National But'cart of Standarda 6911, 1~,)65, pp. 73-77.

[9]

S. Even and R.E. Tarjan, "Network flow and testing graph coEineclivity", SL4'M J. compul. 4, 4, 197fi, pp. 507-518.

[10]

It.N, Gabow and .~l. Stallntalln, "EfHcieut algorithms for graphic matroid int,rs,clion and parity". Automata, Language., and Programming 12t~ ('of Ioqu/um. Lecl~tre .Votes in compuh r Scorner t9,{~ Y. Brauer, ctl., Springer-Verlag, 1985, pp. 210-220.

Digital Library

[11]

H.N. Gabow and R .E.q'arjan. "A linear-time alg, orithm for a special case of disjiont set union' proc. 15th Annual ACM Symp on theory of computing. 1983, pp.216-251.

Digital Library

[12]

B. N Gabow and R. E. Tarjan. "A linear-time algorithm for finding minimum spanning psendoforests" inf proc. Letters, to appear.

Digital Library

[13]

B. N Gabow and R. E. Tarjan. "Algorithms for two boothiieck Ol~ti,~}ization prol~h,lli.4", manuscript.

[14]

H.N. Gabow and B.E. Tarjan. "Almost-optimum spee~l-ilps of algorithms for bipartite tttatching and related problems", Proc. 20ta Annual AUM .,'ymp. on Th. of Computing, 1988.

Digital Library

[15]

D. Gusfiehl. "Connectivity alld edge-disjoint spanning trees", Inf. Proc. ~elters, 16. 1983. pp. 87-89.

[16]

D. Gusfield, "Conlputing the strength of a {mtwork in O(|V|3|e|) time", Tech. Rept. CSE-87-2. Comp. Sci. Div. Univ. Calofrornai Davis. 1987.

[17]

J. Hoperoh and R. Karp, "An n 3/2 algorithm for maximum ~natchirtgsin t~ipartitegraphs", .qt.t3{ .I (:omp. 2.,1, 1973, pl~,. 225:231.

[18]

H. Imar, "Network-fow algorithms for lower-truncatcd transversal polymatroids", J. Op. Res. Soc. of Japan. 26, 3, 19S3.

[19]

M. lri and S. Fujishige, "Use of matroid theory in operations research, circuits and systems theory", Int. J, Systems Sci., L2, 1,L981, pp 27-54.

[20]

A. ltai and M. Rodeh, "The multi-tree approach to reliability in distributed networks", Proc. 25~a Annual S~,mp. on Found, of Comp. Sci., 1984, pp. 137-147.

[21]

G. Kishi and Y. Kajitani, "Maximally distant trees and principal partition of a linear graph", IEEE Trans. Circuit Theorq. C'.T-16, 3, I969, pp. 323-330.

[22]

I,el,nsa~l. A. "A solution 1.o the.Shannol)switching ga~m'" I. Soc. lndust. Appl. Math. 12 (P.)6.t).

[23]

E.L. Lawler, Combinatortal Optimization:,Vetworks and Matrotds, Holt, Rhinehart and Winston, New York, 1976

[24]

L. Lovasz and Y. Yemini, "On generic rigidity in the plane", SIAM I. Alg Disc. meth., 3. 1982, pp. 91-98.

[25]

L.R. Matthews, -Bicircular matroids", Quarterly J. Math. O.tford. '28, 2.1977.pp, 213-22,';,

[26]

C. St J. A. Nash Williams. "Edge-disjoint spanning trees of finite graphs". London math. sec. 36. 1961, pp. 115- 150.

[27]

T. Ohtsuki, Y. Ishizaki and H. Watanabe, "Topological degrecs of freedom mixed analysis of electical nettworks", tEEE 'Trans. current theory, cf. 17, 1. 1970.pp,191-199.

[28]

J.-C. Picar(I and hl, Qimyra~ltl~', "A network flow .solution to some nonlinear 0-1 programming problems, with applications to graph theory", Networks. 12. 1982. pp. 14t-159.

[29]

J. Roskind and R.E. Tarjan, :'A note on finding minimumcost edge-disjoint spanning trees", Math, Op. Res. I0. 4, 1985, pp. 701-708.

[30]

D.D. Sleator and R.E, Tarjan, "A data structure for dyn&mic trees", J. CoreD. and .~ysfem $6 26, 1983, pp.362- 391.

Digital Library

[31]

F-S. Tay, "Rigidity of nlulti-graphs. I. Linking rigid bodio,~ in n-space", .I, comb. Tb. B, 31;, 1984, pp.95-112.

[32]

W. 'F. Tutte. "On th, problem, of decomposing a graph into cm~n,'cted factors", J.London math. soc 36 (1961),pp. 221-230.

[33]

D.J.A. WcLsh, Matroul theory, Acadamic press,london, New York, San Francisco. 1976.

[34]

Herbert H. Wcstermann, "Eflicienr Algorithn~s For Mat roid Sums", Ph.D. Dissertation, Dept. Comp. Sci., Univ. Colorado at Boulder, 1987.

Digital Library

[35]

W. Whiteley, "The ttnion of matroids and the rigidity of frameworks", Champlain Regional College, St. Lambert, Quebec. Canada. 1986. preprint.

[36]

N. White and W. Whil;eley, "The algebraic geometry of motions of bar-and-body franle~vorks", S'IAM .!. Aly. Disc. Meth,. 8, 1~ 1987, pp. 1-32.

Digital Library

Cited By

Blikstad JMukhopadhyay SNanongkai DTu TSaha BServedio R(2023)Fast Algorithms via Dynamic-Oracle MatroidsProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585219(1229-1242)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585219
Christiansen ANowicki KRotenberg ESaha BServedio R(2023)Improved Dynamic Colouring of Sparse GraphsProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585111(1201-1214)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585111
Toko Worou BGaltier J(2016)Fast approximation for computing the fractional arboricity and extraction of communities of a graphDiscrete Applied Mathematics10.1016/j.dam.2014.10.023213:C(179-195)Online publication date: 20-Nov-2016
https://dl.acm.org/doi/10.1016/j.dam.2014.10.023
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Index Terms

Forests, frames, and games: algorithms for matroid sums and applications
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory

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cover image ACM Conferences

STOC '88: Proceedings of the twentieth annual ACM symposium on Theory of computing

January 1988

553 pages

ISBN:0897912640

DOI:10.1145/62212

Chairman:
J'anos Simon
Univ. of Chicago, Illinois

Copyright © 1988 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 January 1988

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STOC88: 1988 Symposium on the Theory of Computing

May 2 - 4, 1988

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STOC '88 Paper Acceptance Rate 53 of 192 submissions, 28%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Blikstad JMukhopadhyay SNanongkai DTu TSaha BServedio R(2023)Fast Algorithms via Dynamic-Oracle MatroidsProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585219(1229-1242)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585219
Christiansen ANowicki KRotenberg ESaha BServedio R(2023)Improved Dynamic Colouring of Sparse GraphsProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585111(1201-1214)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585111
Toko Worou BGaltier J(2016)Fast approximation for computing the fractional arboricity and extraction of communities of a graphDiscrete Applied Mathematics10.1016/j.dam.2014.10.023213:C(179-195)Online publication date: 20-Nov-2016
https://dl.acm.org/doi/10.1016/j.dam.2014.10.023
Farach-Colton MTsai M(2016)Tight Approximations of Degeneracy in Large GraphsLATIN 2016: Theoretical Informatics10.1007/978-3-662-49529-2_32(429-440)Online publication date: 22-Mar-2016
https://doi.org/10.1007/978-3-662-49529-2_32
Censor-Hillel K(2015)Distributed Algorithms as Combinatorial StructuresACM SIGACT News10.1145/2744447.274446146:1(63-76)Online publication date: 9-Mar-2015
https://dl.acm.org/doi/10.1145/2744447.2744461
Williams RGasparri ASoffietti MSukhatme G(2015)Redundantly rigid topologies in decentralized multi-agent networks2015 54th IEEE Conference on Decision and Control (CDC)10.1109/CDC.2015.7403179(6101-6108)Online publication date: Dec-2015
https://doi.org/10.1109/CDC.2015.7403179
Censor-Hillel KGhaffari MKuhn FHalldórsson MDolev S(2014)Distributed connectivity decompositionProceedings of the 2014 ACM symposium on Principles of distributed computing10.1145/2611462.2611491(156-165)Online publication date: 15-Jul-2014
https://dl.acm.org/doi/10.1145/2611462.2611491
Farach-Colton MTsai M(2014)Computing the Degeneracy of Large GraphsLATIN 2014: Theoretical Informatics10.1007/978-3-642-54423-1_22(250-260)Online publication date: 2014
https://doi.org/10.1007/978-3-642-54423-1_22
Lee AStreinu I(2008)Pebble game algorithms and sparse graphsDiscrete Mathematics10.1016/j.disc.2007.07.104308:8(1425-1437)Online publication date: 1-Apr-2008
https://dl.acm.org/doi/10.1016/j.disc.2007.07.104
Kowalik Ł(2006)Approximation scheme for lowest outdegree orientation and graph density measuresProceedings of the 17th international conference on Algorithms and Computation10.1007/11940128_56(557-566)Online publication date: 18-Dec-2006
https://dl.acm.org/doi/10.1007/11940128_56
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