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

N1 - Funding Information:
supported in part by NSF grants CCF-1740858, CCF-1712119, and

PY - 2019

Y1 - 2019

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

KW - Integer programming

KW - Multi-level graph representation

UR - http://www.scopus.com/inward/record.url?scp=85076394792&partnerID=8YFLogxK

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U2 - 10.1007/978-3-030-34029-2_35

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)

SP - 541

EP - 562

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

T2 - Special Event on Analysis of Experimental Algorithms, SEA² 2019

Y2 - 24 June 2019 through 29 June 2019

ER -