Matches in SemOpenAlex for { <https://semopenalex.org/work/W3018984900> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W3018984900 abstract "In this paper, we consider the question of computing sparse subgraphs for any input directed graph $G=(V,E)$ on $n$ vertices and $m$ edges, that preserves reachability and/or strong connectivity structures. We show $O(n+min{|{cal P}|sqrt{n},nsqrt{|{cal P}|}})$ bound on a subgraph that is an $1$-fault-tolerant reachability preserver for a given vertex-pair set ${cal P}subseteq Vtimes V$, i.e., it preserves reachability between any pair of vertices in ${cal P}$ under single edge (or vertex) failure. Our result is a significant improvement over the previous best $O(n |{cal P}|)$ bound obtained as a corollary of single-source reachability preserver construction. We prove our upper bound by exploiting the special structure of single fault-tolerant reachability preserver for any pair, and then considering the interaction among such structures for different pairs. In the lower bound side, we show that a 2-fault-tolerant reachability preserver for a vertex-pair set ${cal P}subseteq Vtimes V$ of size $Omega(n^epsilon)$, for even any arbitrarily small $epsilon$, requires at least $Omega(n^{1+epsilon/8})$ edges. This refutes the existence of linear-sized dual fault-tolerant preservers for reachability for any polynomial sized vertex-pair set. We also present the first sub-quadratic bound of at most $tilde{O}(k 2^k n^{2-1/k})$ size, for strong-connectivity preservers of directed graphs under $k$ failures. To the best of our knowledge no non-trivial bound for this problem was known before, for a general $k$. We get our result by adopting the color-coding technique of Alon, Yuster, and Zwick [JACM'95]." @default.
- W3018984900 created "2020-05-01" @default.
- W3018984900 creator A5024602075 @default.
- W3018984900 creator A5024739923 @default.
- W3018984900 date "2020-04-27" @default.
- W3018984900 modified "2023-09-27" @default.
- W3018984900 title "New Extremal bounds for Reachability and Strong-Connectivity Preservers under failures" @default.
- W3018984900 cites W1577501260 @default.
- W3018984900 cites W1815926779 @default.
- W3018984900 cites W1859011291 @default.
- W3018984900 cites W2018956470 @default.
- W3018984900 cites W2031536548 @default.
- W3018984900 cites W2135290460 @default.
- W3018984900 cites W2413699622 @default.
- W3018984900 cites W2536112642 @default.
- W3018984900 cites W2542527648 @default.
- W3018984900 cites W2569880348 @default.
- W3018984900 cites W2608864129 @default.
- W3018984900 cites W2766479655 @default.
- W3018984900 cites W2775875721 @default.
- W3018984900 cites W2949194358 @default.
- W3018984900 cites W2949301464 @default.
- W3018984900 cites W2952422587 @default.
- W3018984900 cites W2962916904 @default.
- W3018984900 cites W2963664420 @default.
- W3018984900 cites W2972150782 @default.
- W3018984900 hasPublicationYear "2020" @default.
- W3018984900 type Work @default.
- W3018984900 sameAs 3018984900 @default.
- W3018984900 citedByCount "0" @default.
- W3018984900 crossrefType "posted-content" @default.
- W3018984900 hasAuthorship W3018984900A5024602075 @default.
- W3018984900 hasAuthorship W3018984900A5024739923 @default.
- W3018984900 hasConcept C114614502 @default.
- W3018984900 hasConcept C118615104 @default.
- W3018984900 hasConcept C121332964 @default.
- W3018984900 hasConcept C132525143 @default.
- W3018984900 hasConcept C134306372 @default.
- W3018984900 hasConcept C136643341 @default.
- W3018984900 hasConcept C2779557605 @default.
- W3018984900 hasConcept C2780012671 @default.
- W3018984900 hasConcept C33923547 @default.
- W3018984900 hasConcept C62520636 @default.
- W3018984900 hasConcept C77553402 @default.
- W3018984900 hasConcept C80899671 @default.
- W3018984900 hasConceptScore W3018984900C114614502 @default.
- W3018984900 hasConceptScore W3018984900C118615104 @default.
- W3018984900 hasConceptScore W3018984900C121332964 @default.
- W3018984900 hasConceptScore W3018984900C132525143 @default.
- W3018984900 hasConceptScore W3018984900C134306372 @default.
- W3018984900 hasConceptScore W3018984900C136643341 @default.
- W3018984900 hasConceptScore W3018984900C2779557605 @default.
- W3018984900 hasConceptScore W3018984900C2780012671 @default.
- W3018984900 hasConceptScore W3018984900C33923547 @default.
- W3018984900 hasConceptScore W3018984900C62520636 @default.
- W3018984900 hasConceptScore W3018984900C77553402 @default.
- W3018984900 hasConceptScore W3018984900C80899671 @default.
- W3018984900 hasLocation W30189849001 @default.
- W3018984900 hasOpenAccess W3018984900 @default.
- W3018984900 hasPrimaryLocation W30189849001 @default.
- W3018984900 hasRelatedWork W1498923031 @default.
- W3018984900 hasRelatedWork W1527014360 @default.
- W3018984900 hasRelatedWork W1555792552 @default.
- W3018984900 hasRelatedWork W1778534330 @default.
- W3018984900 hasRelatedWork W2093361910 @default.
- W3018984900 hasRelatedWork W2406039934 @default.
- W3018984900 hasRelatedWork W2413699622 @default.
- W3018984900 hasRelatedWork W2611126464 @default.
- W3018984900 hasRelatedWork W2907331504 @default.
- W3018984900 hasRelatedWork W2950319843 @default.
- W3018984900 hasRelatedWork W2950939203 @default.
- W3018984900 hasRelatedWork W2953062565 @default.
- W3018984900 hasRelatedWork W2963583531 @default.
- W3018984900 hasRelatedWork W2991205088 @default.
- W3018984900 hasRelatedWork W3034442942 @default.
- W3018984900 hasRelatedWork W3038069570 @default.
- W3018984900 hasRelatedWork W3089482228 @default.
- W3018984900 hasRelatedWork W3092127594 @default.
- W3018984900 hasRelatedWork W3104055895 @default.
- W3018984900 hasRelatedWork W2460394128 @default.
- W3018984900 isParatext "false" @default.
- W3018984900 isRetracted "false" @default.
- W3018984900 magId "3018984900" @default.
- W3018984900 workType "article" @default.