TY - GEN

T1 - δ-Greedy t-spanner

AU - On, Gali Bar

AU - Carmi, Paz

N1 - Funding Information:
The research is partially supported by the Lynn and William Frankel Center for Computer Science.
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We introduce a new geometric spanner, δ-Greedy, whose construction is based on a generalization of the known Path-Greedy and Gap-Greedy spanners. The δ-Greedy spanner combines the most desirable properties of geometric spanners both in theory and in practice. More specifically, it has the same theoretical and practical properties as the Path-Greedy spanner: a natural definition, small degree, linear number of edges, low weight, and strong (1+ε)-spanner for every ε > 0. The δ-Greedy algorithm is an improvement over the Path-Greedy algorithm with respect to the number of shortest path queries and hence with respect to its construction time. We show how to construct such a spanner for a set of n points in the plane in O(n2 log n) time. The δ-Greedy spanner has an additional parameter, δ, which indicates how close it is to the Path-Greedy spanner on the account of the number of shortest path queries. For δ = t the output spanner is identical to the Path-Greedy spanner, while the number of shortest path queries is, in practice, linear. Finally, we show that for a set of n points placed independently at random in a unit square the expected construction time of the δ-Greedy algorithm is O(n log n). Our analysis indicates that the δ-Greedy spanner gives the best results among the known spanners of expected O(n log n) time for random point sets. Moreover, analysis implies that by setting δ = t, the δ-Greedy algorithm provides a spanner identical to the Path-Greedy spanner in expected O(n log n) time.

AB - We introduce a new geometric spanner, δ-Greedy, whose construction is based on a generalization of the known Path-Greedy and Gap-Greedy spanners. The δ-Greedy spanner combines the most desirable properties of geometric spanners both in theory and in practice. More specifically, it has the same theoretical and practical properties as the Path-Greedy spanner: a natural definition, small degree, linear number of edges, low weight, and strong (1+ε)-spanner for every ε > 0. The δ-Greedy algorithm is an improvement over the Path-Greedy algorithm with respect to the number of shortest path queries and hence with respect to its construction time. We show how to construct such a spanner for a set of n points in the plane in O(n2 log n) time. The δ-Greedy spanner has an additional parameter, δ, which indicates how close it is to the Path-Greedy spanner on the account of the number of shortest path queries. For δ = t the output spanner is identical to the Path-Greedy spanner, while the number of shortest path queries is, in practice, linear. Finally, we show that for a set of n points placed independently at random in a unit square the expected construction time of the δ-Greedy algorithm is O(n log n). Our analysis indicates that the δ-Greedy spanner gives the best results among the known spanners of expected O(n log n) time for random point sets. Moreover, analysis implies that by setting δ = t, the δ-Greedy algorithm provides a spanner identical to the Path-Greedy spanner in expected O(n log n) time.

UR - http://www.scopus.com/inward/record.url?scp=85025175010&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-62127-2_8

DO - 10.1007/978-3-319-62127-2_8

M3 - Conference contribution

AN - SCOPUS:85025175010

SN - 9783319621265

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

SP - 85

EP - 96

BT - Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings

A2 - Ellen, Faith

A2 - Kolokolova, Antonina

A2 - Sack, Jorg-Rudiger

PB - Springer Verlag

T2 - 15th International Symposium on Algorithms and Data Structures, WADS 2017

Y2 - 31 July 2017 through 2 August 2017

ER -