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 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
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
KW - Integer programming
KW - Multi-level graph representation
UR - http://www.scopus.com/inward/record.url?scp=85076394792&partnerID=8YFLogxK
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 -
