Graph orientation with edge modifications

Yuichi Asahiro, Jesper Andreas Jansson, Eiji Miyano, Hirotaka Ono, Sandhya Thekkumpadan Puthiyaveedu

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationFrontiers in Algorithmics - 13th International Workshop, FAW 2019, Proceedings
EditorsYijia Chen, Xiaotie Deng, Mei Lu
Number of pages13
ISBN (Print)9783030181253
Publication statusPublished - 1 Jan 2019
Event13th International Workshop on Frontiers in Algorithmics, FAW 2019 - Sanya, China
Duration: 29 Apr 20193 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11458 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Workshop on Frontiers in Algorithmics, FAW 2019


  • Computational complexity
  • Graph orientation
  • Greedy algorithm
  • Inapproximability
  • Load balancing
  • Maximum flow

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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