The color-balanced spanning tree problem

Štefan Berežný; Vladimír Lacko

Kybernetika (2005)

  • Volume: 41, Issue: 4, page [539]-546
  • ISSN: 0023-5954

Abstract

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Suppose a graph G = ( V , E ) whose edges are partitioned into p disjoint categories (colors) is given. In the color-balanced spanning tree problem a spanning tree is looked for that minimizes the variability in the number of edges from different categories. We show that polynomiality of this problem depends on the number p of categories and present some polynomial algorithm.

How to cite

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Berežný, Štefan, and Lacko, Vladimír. "The color-balanced spanning tree problem." Kybernetika 41.4 (2005): [539]-546. <http://eudml.org/doc/33771>.

@article{Berežný2005,
abstract = {Suppose a graph $G=(V,E)$ whose edges are partitioned into $p$ disjoint categories (colors) is given. In the color-balanced spanning tree problem a spanning tree is looked for that minimizes the variability in the number of edges from different categories. We show that polynomiality of this problem depends on the number $p$ of categories and present some polynomial algorithm.},
author = {Berežný, Štefan, Lacko, Vladimír},
journal = {Kybernetika},
keywords = {spanning tree; matroids; algorithms; NP-completeness; spanning tree; matroids; polynomial algorithms; NP-completeness; edge partition},
language = {eng},
number = {4},
pages = {[539]-546},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The color-balanced spanning tree problem},
url = {http://eudml.org/doc/33771},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Berežný, Štefan
AU - Lacko, Vladimír
TI - The color-balanced spanning tree problem
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 4
SP - [539]
EP - 546
AB - Suppose a graph $G=(V,E)$ whose edges are partitioned into $p$ disjoint categories (colors) is given. In the color-balanced spanning tree problem a spanning tree is looked for that minimizes the variability in the number of edges from different categories. We show that polynomiality of this problem depends on the number $p$ of categories and present some polynomial algorithm.
LA - eng
KW - spanning tree; matroids; algorithms; NP-completeness; spanning tree; matroids; polynomial algorithms; NP-completeness; edge partition
UR - http://eudml.org/doc/33771
ER -

References

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  2. Berežný Š., Cechlárová, K., Lacko V., Optimization problems on graphs with categorization of edges, In: Proc. SOR 2001 (V. Rupnik, L. Zadnik-Stirn, and S. Drobne, eds.), Slovenian Society Informatika – Section for Operational Research, Predvor Slovenia 2001, pp. 171–176 
  3. Berežný Š., Cechlárová, K., Lacko V., A polynomially solvable case of optimization problems on graphs with categorization of edges, In: Proc. 17th Internat. Conference Mathematical Methods in Economics ’99 (J. Plešingr, ed.), Czech Society for Operations Research, Jindřichův Hradec 1999, pp. 25–31 (1999) 
  4. Berežný Š., Lacko V., 10.7151/dmgt.1182, Discuss. Math. Graph Theory 23 (2003), 5–21 Zbl1050.05112MR1987558DOI10.7151/dmgt.1182
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  6. Lawler E. L., Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York 1976 Zbl1058.90057MR0439106
  7. Punnen A. P., 10.1016/0167-6377(92)90069-F, Oper. Res. Lett. 12 (1992), 89–95 (1992) Zbl0768.90077MR1188371DOI10.1016/0167-6377(92)90069-F
  8. Richey M. B., Punnen A. P., 10.1016/0166-218X(92)90165-7, Discrete Appl. Math. 39 (1992), 147–153 (1992) MR1184685DOI10.1016/0166-218X(92)90165-7
  9. Rosen K. H., Michaels J. G., Handbook of Discrete and Combinatorial Mathematics, CRC Press, New York 1997 Zbl1044.00002MR1725200

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