Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

On the complexity of edge-colored subgraph partitioning problems in network optimization

Abstract : Network models allow one to deal with massive data sets using some standard concepts from graph theory. Understanding and investigating the structural properties of a certain data set is a crucial task in many practical applications of network optimization. Recently, labeled network optimization over colored graphs has been extensively studied. Given a (not necessarily properly) edge-colored graph $G=(V,E)$, a subgraph $H$ is said to be monochromatic if all its edges have the same color, and called multicolored if all its edges have distinct colors. The monochromatic clique and multicolored cycle partition problems have important applications in the problems of network optimization arising in information science and operations research. We investigate the computational complexity of the problems of determining the minimum number of monochromatic cliques or multicolored cycles that, respectively, partition $V(G)$. We show that the minimum monochromatic clique partition problem is APX-hard on monochromatic-diamond-free graphs, and APX-complete on monochromatic-diamond-free graphs in which the size of a maximum monochromatic clique is bounded by a constant. We also show that the minimum multicolored cycle partition problem is NP-complete, even if the input graph $G$ is triangle-free. Moreover, for the weighted version of the minimum monochromatic clique partition problem on monochromatic-diamond-free graphs, we derive an approximation algorithm with (tight) approximation guarantee ln $|V(G)|+1$.
Document type :
Journal articles
Complete list of metadata

Cited literature [34 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, August 16, 2016 - 3:16:55 PM
Last modification on : Thursday, August 29, 2019 - 5:02:12 PM
Long-term archiving on: : Thursday, November 17, 2016 - 10:55:16 AM


Explicit agreement for this submission




Xiaoyan Zhang, Zan-Bo Zhang, Hajo Broersma, Xuelian Wen. On the complexity of edge-colored subgraph partitioning problems in network optimization. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.227-244. ⟨10.46298/dmtcs.2159⟩. ⟨hal-01352853⟩



Record views


Files downloads