eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
24:1
24:11
10.4230/LIPIcs.ICALP.2020.24
article
Roundtrip Spanners with (2k-1) Stretch
Cen, Ruoxu
1
Duan, Ran
1
Gu, Yong
1
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
A roundtrip spanner of a directed graph G is a subgraph of G preserving roundtrip distances approximately for all pairs of vertices. Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs. For a directed graph with real edge weights in [1,W], we first propose a new deterministic algorithm that constructs a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log (nW)) edges for every integer k > 1, then remove the dependence of size on W to give a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log n) edges. While keeping the edge size small, our result improves the previous 2k+ε stretch roundtrip spanners in directed graphs [Roditty, Thorup, Zwick'02; Zhu, Lam'18], and almost matches the undirected (2k-1)-spanner with O(n^(1+1/k)) edges [Althöfer et al. '93] when k is a constant, which is optimal under Erdös conjecture.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.24/LIPIcs.ICALP.2020.24.pdf
Graph theory
Deterministic algorithm
Roundtrip spanners