Balanced problems on graphs with categorization of edges

Štefan Berežný; Vladimír Lacko

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 1, page 5-21
  • ISSN: 2083-5892

Abstract

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Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: L ₅ ( D ) = m a x 1 ≤ i ≤ p ( m a x e ∈ S i ∩ D w ( e ) - m i n e ∈ S i ∩ D w ( e ) ) For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary and for fixed number of categories.

How to cite

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Štefan Berežný, and Vladimír Lacko. "Balanced problems on graphs with categorization of edges." Discussiones Mathematicae Graph Theory 23.1 (2003): 5-21. <http://eudml.org/doc/270439>.

@article{ŠtefanBerežný2003,
abstract = {Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: $L₅(D) = max_\{1≤i≤p\} (max_\{e ∈ S_i ∩ D\} w(e) - min_\{e ∈ S_i ∩ D\} w(e))$ For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary and for fixed number of categories.},
author = {Štefan Berežný, Vladimír Lacko},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {algorithms on graphs; categorization of edges; NP-completeness; optimization problems},
language = {eng},
number = {1},
pages = {5-21},
title = {Balanced problems on graphs with categorization of edges},
url = {http://eudml.org/doc/270439},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Štefan Berežný
AU - Vladimír Lacko
TI - Balanced problems on graphs with categorization of edges
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 1
SP - 5
EP - 21
AB - Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: $L₅(D) = max_{1≤i≤p} (max_{e ∈ S_i ∩ D} w(e) - min_{e ∈ S_i ∩ D} w(e))$ For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary and for fixed number of categories.
LA - eng
KW - algorithms on graphs; categorization of edges; NP-completeness; optimization problems
UR - http://eudml.org/doc/270439
ER -

References

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  10. [10] V. Lacko, Persistency in Traveling Salesman Problem on Halin graphs, Discuss. Math. Graph Theory 20 (2000) 231-242, doi: 10.7151/dmgt.1122. Zbl0982.05064
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