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

doi:10.1007/978-3-030-34029-2_35

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 proceeding › Conference contribution › peer-review

5 Scopus citations

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 language	English
Title of host publication	Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers
Editors	Ilias Kotsireas, Panos Pardalos, Arsenis Tsokas, Konstantinos E. Parsopoulos, Dimitris Souravlias
Publisher	Springer
Pages	541-562
Number of pages	22
ISBN (Print)	9783030340285
DOIs	https://doi.org/10.1007/978-3-030-34029-2_35
State	Published - 1 Jan 2019
Externally published	Yes
Event	Special Event on Analysis of Experimental Algorithms, SEA² 2019 - Kalamata, Greece Duration: 24 Jun 2019 → 29 Jun 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11544 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Special Event on Analysis of Experimental Algorithms, SEA² 2019
Country/Territory	Greece
City	Kalamata
Period	24/06/19 → 29/06/19

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 11 Sustainable Cities and Communities

Keywords

Graph spanners
Integer programming
Multi-level graph representation

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-34029-2_35

Cite this

Ahmed, R., Hamm, K., Latifi Jebelli, M. J., Kobourov, S., Sahneh, F. D., & Spence, R. (2019). Approximation Algorithms and an Integer Program for Multi-level Graph Spanners. In I. Kotsireas, P. Pardalos, A. Tsokas, K. E. Parsopoulos, & D. Souravlias (Eds.), Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers (pp. 541-562). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11544 LNCS). Springer. https://doi.org/10.1007/978-3-030-34029-2_35

Ahmed, Reyan ; Hamm, Keaton ; Latifi Jebelli, Mohammad Javad et al. / Approximation Algorithms and an Integer Program for Multi-level Graph Spanners. Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers . editor / Ilias Kotsireas ; Panos Pardalos ; Arsenis Tsokas ; Konstantinos E. Parsopoulos ; Dimitris Souravlias. Springer, 2019. pp. 541-562 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{6f6413ec67344487992fe32cbdf10efb,

title = "Approximation Algorithms and an Integer Program for Multi-level Graph Spanners",

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.",

keywords = "Graph spanners, Integer programming, Multi-level graph representation",

author = "Reyan Ahmed and Keaton Hamm and \{Latifi Jebelli\}, \{Mohammad Javad\} and Stephen Kobourov and Sahneh, \{Faryad Darabi\} and Richard Spence",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; Special Event on Analysis of Experimental Algorithms, SEA² 2019 ; Conference date: 24-06-2019 Through 29-06-2019",

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doi = "10.1007/978-3-030-34029-2\_35",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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editor = "Ilias Kotsireas and Panos Pardalos and Arsenis Tsokas and Parsopoulos, \{Konstantinos E.\} and Dimitris Souravlias",

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Ahmed, R, Hamm, K, Latifi Jebelli, MJ, Kobourov, S, Sahneh, FD & Spence, R 2019, Approximation Algorithms and an Integer Program for Multi-level Graph Spanners. in I Kotsireas, P Pardalos, A Tsokas, KE Parsopoulos & D Souravlias (eds), Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers . Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11544 LNCS, Springer, pp. 541-562, Special Event on Analysis of Experimental Algorithms, SEA² 2019, Kalamata, Greece, 24/06/19. https://doi.org/10.1007/978-3-030-34029-2_35

Approximation Algorithms and an Integer Program for Multi-level Graph Spanners. / Ahmed, Reyan; Hamm, Keaton; Latifi Jebelli, Mohammad Javad et al.
Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers . ed. / Ilias Kotsireas; Panos Pardalos; Arsenis Tsokas; Konstantinos E. Parsopoulos; Dimitris Souravlias. Springer, 2019. p. 541-562 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11544 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Approximation Algorithms and an Integer Program for Multi-level Graph Spanners

AU - Ahmed, Reyan

AU - Hamm, Keaton

AU - Latifi Jebelli, Mohammad Javad

AU - Kobourov, Stephen

AU - Sahneh, Faryad Darabi

AU - Spence, Richard

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Graph spanners

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DO - 10.1007/978-3-030-34029-2_35

M3 - Conference contribution

AN - SCOPUS:85076394792

SN - 9783030340285

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers

A2 - Kotsireas, Ilias

A2 - Pardalos, Panos

A2 - Tsokas, Arsenis

A2 - Parsopoulos, Konstantinos E.

A2 - Souravlias, Dimitris

PB - Springer

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Y2 - 24 June 2019 through 29 June 2019

ER -

Ahmed R, Hamm K, Latifi Jebelli MJ, Kobourov S, Sahneh FD, Spence R. Approximation Algorithms and an Integer Program for Multi-level Graph Spanners. In Kotsireas I, Pardalos P, Tsokas A, Parsopoulos KE, Souravlias D, editors, Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers . Springer. 2019. p. 541-562. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-34029-2_35

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

Abstract

Publication series

Conference

UN SDGs

Keywords

ASJC Scopus subject areas

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