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- W2951028132 abstract "We introduce a new geometric spanner, $delta$-Greedy, whose construction is based on a generalization of the known Path-Greedy and Gap-Greedy spanners. The $delta$-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 $(1+varepsilon)$-spanner for every $varepsilon>0$. The $delta$-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 $O(n^2 log n)$ time. The $delta$-Greedy spanner has an additional parameter, $delta$, which indicates how close it is to the Path-Greedy spanner on the account of the number of shortest path queries. For $delta = t$ 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 $delta$-Greedy algorithm is $O(n log n)$. Our analysis indicates that the $delta$-Greedy spanner gives the best results among the known spanners of expected $O(n log n)$ time for random point sets. Moreover, the analysis implies that by setting $delta = t$, the $delta$-Greedy algorithm provides a spanner identical to the Path-Greedy spanner in expected $O(n log n)$ time." @default.
- W2951028132 created "2019-06-27" @default.
- W2951028132 creator A5026094478 @default.
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- W2951028132 date "2017-02-20" @default.
- W2951028132 modified "2023-09-27" @default.
- W2951028132 title "$delta$-Greedy $t$-spanner" @default.
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