Matches in SemOpenAlex for { <https://semopenalex.org/work/W2999762092> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2999762092 endingPage "129" @default.
- W2999762092 startingPage "101" @default.
- W2999762092 abstract "We study the following version of cut sparsification. Given a large edge-weighted network $G$ with $k$ terminal vertices, compress it into a smaller network $H$ with the same terminals, such that every minimum terminal cut in $H$ approximates the corresponding one in $G$, up to a factor $qgeq 1$ that is called the quality. (The case $q=1$ is known also as a mimicking network.) We provide new insights about the structure of minimum terminal cuts, leading to new results for cut sparsifiers of planar graphs. Our first contribution identifies a subset of the minimum terminal cuts, which we call elementary, that generates all the others. Consequently, $H$ is a cut sparsifier if and only if it preserves all the elementary terminal cuts (up to this factor $q$). Our second and main contribution is to refine the known bounds in terms of $gamma=gamma(G)$, which is defined as the minimum number of faces that are incident to all the terminals in a planar graph $G$. We prove that the number of elementary terminal cuts is $O((2k/gamma)^{2gamma})$ (compared to $O(2^k)$ terminal cuts) and furthermore obtain a mimicking network of size $O(gamma 2^{2gamma} k^4)$, which is near-optimal as a function of $gamma$. Our third contribution is a duality between cut sparsification and distance sparsification for certain planar graphs, when the sparsifier $H$ is required to be a minor of $G$. This duality connects problems that were previously studied separately, implying new results, new proofs of known results, and equivalences between open gaps." @default.
- W2999762092 created "2020-01-23" @default.
- W2999762092 creator A5037378898 @default.
- W2999762092 creator A5086550216 @default.
- W2999762092 date "2020-01-01" @default.
- W2999762092 modified "2023-10-16" @default.
- W2999762092 title "Refined Vertex Sparsifiers of Planar Graphs" @default.
- W2999762092 cites W1543491698 @default.
- W2999762092 cites W1968729061 @default.
- W2999762092 cites W1989626562 @default.
- W2999762092 cites W2017713020 @default.
- W2999762092 cites W2018963243 @default.
- W2999762092 cites W2036743540 @default.
- W2999762092 cites W2039202283 @default.
- W2999762092 cites W2039305125 @default.
- W2999762092 cites W2040444410 @default.
- W2999762092 cites W2065759448 @default.
- W2999762092 cites W2068727899 @default.
- W2999762092 cites W2129575457 @default.
- W2999762092 cites W2401176303 @default.
- W2999762092 cites W2568140225 @default.
- W2999762092 cites W2569472613 @default.
- W2999762092 cites W3100089996 @default.
- W2999762092 cites W3160409744 @default.
- W2999762092 doi "https://doi.org/10.1137/17m1151225" @default.
- W2999762092 hasPublicationYear "2020" @default.
- W2999762092 type Work @default.
- W2999762092 sameAs 2999762092 @default.
- W2999762092 citedByCount "5" @default.
- W2999762092 countsByYear W29997620922017 @default.
- W2999762092 countsByYear W29997620922020 @default.
- W2999762092 countsByYear W29997620922021 @default.
- W2999762092 countsByYear W29997620922022 @default.
- W2999762092 crossrefType "journal-article" @default.
- W2999762092 hasAuthorship W2999762092A5037378898 @default.
- W2999762092 hasAuthorship W2999762092A5086550216 @default.
- W2999762092 hasBestOaLocation W29997620922 @default.
- W2999762092 hasConcept C101837359 @default.
- W2999762092 hasConcept C108710211 @default.
- W2999762092 hasConcept C114614502 @default.
- W2999762092 hasConcept C118615104 @default.
- W2999762092 hasConcept C121684516 @default.
- W2999762092 hasConcept C132525143 @default.
- W2999762092 hasConcept C134786449 @default.
- W2999762092 hasConcept C2524010 @default.
- W2999762092 hasConcept C2778023678 @default.
- W2999762092 hasConcept C2778753846 @default.
- W2999762092 hasConcept C2779664074 @default.
- W2999762092 hasConcept C33923547 @default.
- W2999762092 hasConcept C41008148 @default.
- W2999762092 hasConcept C76155785 @default.
- W2999762092 hasConcept C80899671 @default.
- W2999762092 hasConceptScore W2999762092C101837359 @default.
- W2999762092 hasConceptScore W2999762092C108710211 @default.
- W2999762092 hasConceptScore W2999762092C114614502 @default.
- W2999762092 hasConceptScore W2999762092C118615104 @default.
- W2999762092 hasConceptScore W2999762092C121684516 @default.
- W2999762092 hasConceptScore W2999762092C132525143 @default.
- W2999762092 hasConceptScore W2999762092C134786449 @default.
- W2999762092 hasConceptScore W2999762092C2524010 @default.
- W2999762092 hasConceptScore W2999762092C2778023678 @default.
- W2999762092 hasConceptScore W2999762092C2778753846 @default.
- W2999762092 hasConceptScore W2999762092C2779664074 @default.
- W2999762092 hasConceptScore W2999762092C33923547 @default.
- W2999762092 hasConceptScore W2999762092C41008148 @default.
- W2999762092 hasConceptScore W2999762092C76155785 @default.
- W2999762092 hasConceptScore W2999762092C80899671 @default.
- W2999762092 hasFunder F4320320878 @default.
- W2999762092 hasFunder F4320322252 @default.
- W2999762092 hasIssue "1" @default.
- W2999762092 hasLocation W29997620921 @default.
- W2999762092 hasLocation W29997620922 @default.
- W2999762092 hasOpenAccess W2999762092 @default.
- W2999762092 hasPrimaryLocation W29997620921 @default.
- W2999762092 hasRelatedWork W2006947206 @default.
- W2999762092 hasRelatedWork W2019255250 @default.
- W2999762092 hasRelatedWork W2374778222 @default.
- W2999762092 hasRelatedWork W2400746548 @default.
- W2999762092 hasRelatedWork W2983736839 @default.
- W2999762092 hasRelatedWork W3015759841 @default.
- W2999762092 hasRelatedWork W4206560000 @default.
- W2999762092 hasRelatedWork W4226175138 @default.
- W2999762092 hasRelatedWork W4287756435 @default.
- W2999762092 hasRelatedWork W4295995756 @default.
- W2999762092 hasVolume "34" @default.
- W2999762092 isParatext "false" @default.
- W2999762092 isRetracted "false" @default.
- W2999762092 magId "2999762092" @default.
- W2999762092 workType "article" @default.