Graph Orientation with Edge Modifications
| Autor: | Eiji Miyano, Yuichi Asahiro, Jesper Jansson, Hirotaka Ono, T P Sandhya |
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| Rok vydání: | 2021 |
| Předmět: |
Epigraph
021103 operations research Computational complexity theory Maximum flow problem 0211 other engineering and technologies 0102 computer and information sciences 02 engineering and technology Orientation (graph theory) Type (model theory) Edge (geometry) 01 natural sciences Combinatorics 010201 computation theory & mathematics TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Computer Science (miscellaneous) Graph (abstract data type) Undirected graph MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | International Journal of Foundations of Computer Science. 32:209-233 |
| ISSN: | 1793-6373 0129-0541 |
| DOI: | 10.1142/s012905412150012x |
| Popis: | The goal of an outdegree-constrained edge-modification problem is to find a spanning subgraph or supergraph [Formula: see text] of an input undirected graph [Formula: see text] such that either: (Type I) the number of edges in [Formula: see text] is minimized or maximized and [Formula: see text] can be oriented to satisfy some specified constraints on the vertices’ resulting outdegrees; or: (Type II) among all subgraphs or supergraphs of [Formula: see text] that can be constructed by deleting or inserting a fixed number of edges, [Formula: see text] 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) [Formula: see text]-DEL-MAX, [Formula: see text]-INS-MIN, [Formula: see text]-INS-MAX, and [Formula: see text]-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. |
| Databáze: | OpenAIRE |
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