TY - GEN
T1 - New fault tolerant subset preservers
AU - Bodwin, Greg
AU - Choudhary, Keerti
AU - Parter, Merav
AU - Shahar, Noa
N1 - Publisher Copyright: © Greg Bodwin, Keerti Choudhary, Merav Parter, and Noa Shahar; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Fault tolerant distance preservers are sparse subgraphs that preserve distances between given pairs of nodes under edge or vertex failures. In this paper, we present the first non-trivial constructions of subset distance preservers, which preserve all distances among a subset of nodes S, that can handle either an edge or a vertex fault. For an n-vertex undirected weighted graph or weighted DAG G = (V, E) and S ⊆ V , we present a construction of a subset preserver with Oe(|S|n) edges that is resilient to a single fault. In the single pair case (|S| = 2), the bound improves to O(n). We further provide a nearly-matching lower bound of Ω(|S|n) in either setting, and we show that the same lower bound holds conditionally even if attention is restricted to unweighted graphs. For an n-vertex directed unweighted graph G = (V, E) and r ∈ V, S ⊆ V ,we present a construction of a preserver of distances in {r} × S with Oe(n4/3|S|5/6) edges that is resilient to a single fault. In the case |S| = 1 the bound improves to O(n4/3), and for this case we provide another matching conditional lower bound. For an n-vertex directed weighted graph G = (V, E) and r ∈ V, S ⊆ V , we present a construction of a preserver of distances in {r} × S with Oe(n3/2|S|3/4) edges that is resilient to a single vertex fault. (It was proved in [14] that the bound improves to O(n3/2) when |S| = 1, and that this is conditionally tight).
AB - Fault tolerant distance preservers are sparse subgraphs that preserve distances between given pairs of nodes under edge or vertex failures. In this paper, we present the first non-trivial constructions of subset distance preservers, which preserve all distances among a subset of nodes S, that can handle either an edge or a vertex fault. For an n-vertex undirected weighted graph or weighted DAG G = (V, E) and S ⊆ V , we present a construction of a subset preserver with Oe(|S|n) edges that is resilient to a single fault. In the single pair case (|S| = 2), the bound improves to O(n). We further provide a nearly-matching lower bound of Ω(|S|n) in either setting, and we show that the same lower bound holds conditionally even if attention is restricted to unweighted graphs. For an n-vertex directed unweighted graph G = (V, E) and r ∈ V, S ⊆ V ,we present a construction of a preserver of distances in {r} × S with Oe(n4/3|S|5/6) edges that is resilient to a single fault. In the case |S| = 1 the bound improves to O(n4/3), and for this case we provide another matching conditional lower bound. For an n-vertex directed weighted graph G = (V, E) and r ∈ V, S ⊆ V , we present a construction of a preserver of distances in {r} × S with Oe(n3/2|S|3/4) edges that is resilient to a single vertex fault. (It was proved in [14] that the bound improves to O(n3/2) when |S| = 1, and that this is conditionally tight).
KW - Distances
KW - Fault-tolerance
KW - Subset Preservers
UR - http://www.scopus.com/inward/record.url?scp=85089350708&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2020.15
DO - 10.4230/LIPIcs.ICALP.2020.15
M3 - منشور من مؤتمر
VL - 168
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
A2 - Czumaj, Artur
A2 - Dawar, Anuj
A2 - Merelli, Emanuela
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Y2 - 8 July 2020 through 11 July 2020
ER -