Approximation Algorithms and an Integer Program for Multi-level Graph Spanners

Reyan Ahmed, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, Faryad Darabi Sahneh, Richard Spence

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a weighted graph G(V, E) and a subgraph H is a t–spanner of G if the lengths of shortest paths in G are preserved in H up to a multiplicative factor of t. The subsetwise spanner problem aims to preserve distances in G for only a subset of the vertices. We generalize the minimum-cost subsetwise spanner problem to one where vertices appear on multiple levels, which we call the multi-level graph spanner (MLGS) problem, and describe two simple heuristics. Applications of this problem include road/network building and multi-level graph visualization, especially where vertices may require different grades of service. We formulate a 0–1 integer linear program (ILP) of size for the more general minimum pairwise spanner problem, which resolves an open question by Sigurd and Zachariasen on whether this problem admits a useful polynomial-size ILP. We extend this ILP formulation to the MLGS problem, and evaluate the heuristic and ILP performance on random graphs of up to 100 vertices and 500 edges.

Original languageEnglish (US)
Title of host publicationAnalysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers
EditorsIlias Kotsireas, Panos Pardalos, Arsenis Tsokas, Konstantinos E. Parsopoulos, Dimitris Souravlias
PublisherSpringer
Pages541-562
Number of pages22
ISBN (Print)9783030340285
DOIs
StatePublished - 2019
EventSpecial Event on Analysis of Experimental Algorithms, SEA² 2019 - Kalamata, Greece
Duration: Jun 24 2019Jun 29 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11544 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceSpecial Event on Analysis of Experimental Algorithms, SEA² 2019
Country/TerritoryGreece
CityKalamata
Period6/24/196/29/19

Keywords

  • Graph spanners
  • Integer programming
  • Multi-level graph representation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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