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Graph Orientation with Edge Modifications

  • Yuichi AsahiroEmail author
  • Jesper Jansson
  • Eiji Miyano
  • Hirotaka Ono
  • Sandhya T. P.
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11458)

Abstract

The goal of an outdegree-constrained edge-modification problem is to find a spanning subgraph or supergraph H of an input undirected graph G such that either: (Type I) the number of edges in H is minimized or maximized and H can be oriented to satisfy some specified constraints on the vertices’ resulting outdegrees; or: (Type II) the maximum or minimum outdegree of all vertices under an optimal orientation of H is minimum or maximum among all subgraphs or supergraphs of G that can be constructed by deleting or inserting a fixed number of edges. This paper introduces eight new outdegree-constrained edge-modification problems related to load balancing called (Type I) MIN-DEL-MAX, MIN-INS-MIN, MAX-INS-MAX, and MAX-DEL-MIN and (Type II) p-DEL-MAX, p-INS-MIN, p-INS-MAX, and p-DEL-MIN. We first present a framework that provides algorithms for solving all eight problems in polynomial time on unweighted graphs. Next we investigate the inapproximability of the edge-weighted versions of the problems, and design polynomial-time algorithms for six of the problems on edge-weighted trees.

Keywords

Graph orientation Maximum flow Computational complexity Inapproximability Greedy algorithm Load balancing 

Notes

Acknowledgments

This work was partially supported by JSPS KAKENHI Grant Numbers JP17K00016 and JP17K00024, and JST CREST JPMJR1402.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yuichi Asahiro
    • 1
    Email author
  • Jesper Jansson
    • 2
  • Eiji Miyano
    • 3
  • Hirotaka Ono
    • 4
  • Sandhya T. P.
    • 2
  1. 1.Department of Information ScienceKyushu Sangyo UniversityFukuokaJapan
  2. 2.The Hong Kong Polytechnic UniversityKowloonHong Kong
  3. 3.Department of Artificial IntelligenceKyushu Institute of TechnologyIizukaJapan
  4. 4.Graduate School of InformaticsNagoya UniversityNagoyaJapan

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