Graph Orientation with Edge Modifications

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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) among all subgraphs or supergraphs of G that can be constructed by deleting or inserting a fixed number of edges, H admits an orientation optimizing some objective involving the vertices' outdegrees. 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. In each of the eight problems, the input is a graph and the goal is to delete or insert edges so that the resulting graph has an orientation in which the maximum outdegree (taken over all vertices) is small or the minimum outdegree is large. 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
Pages (from-to)209-233
Number of pages25
JournalInternational Journal of Foundations of Computer Science
Issue number2
Publication statusPublished - 2021


  • computational complexity
  • Graph orientation
  • inapproximability
  • load balancing
  • maximum flow

ASJC Scopus subject areas

  • Computer Science (miscellaneous)


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