Matches in SemOpenAlex for { <https://semopenalex.org/work/W4299527437> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W4299527437 abstract "Given a large edge-weighted network $G$ with $k$ terminal vertices, we wish to compress it and store, using little memory, the value of the minimum cut (or equivalently, maximum flow) between every bipartition of terminals. One appealing methodology to implement a compression of $G$ is to construct a emph{mimicking network}: a small network $G'$ with the same $k$ terminals, in which the minimum cut value between every bipartition of terminals is the same as in $G$. This notion was introduced by Hagerup, Katajainen, Nishimura, and Ragde [JCSS '98], who proved that such $G'$ of size at most $2^{2^k}$ always exists. Obviously, by having access to the smaller network $G'$, certain computations involving cuts can be carried out much more efficiently. We provide several new bounds, which together narrow the previously known gap from doubly-exponential to only singly-exponential, both for planar and for general graphs. Our first and main result is that every $k$-terminal planar network admits a mimicking network $G'$ of size $O(k^2 2^{2k})$, which is moreover a minor of $G$. On the other hand, some planar networks $G$ require $|E(G')| ge Omega(k^2)$. For general networks, we show that certain bipartite graphs only admit mimicking networks of size $|V(G')| geq 2^{Omega(k)}$, and moreover, every data structure that stores the minimum cut value between all bipartitions of the terminals must use $2^{Omega(k)}$ machine words." @default.
- W4299527437 created "2022-10-02" @default.
- W4299527437 creator A5023940060 @default.
- W4299527437 creator A5037378898 @default.
- W4299527437 date "2012-07-26" @default.
- W4299527437 modified "2023-09-26" @default.
- W4299527437 title "Mimicking Networks and Succinct Representations of Terminal Cuts" @default.
- W4299527437 doi "https://doi.org/10.48550/arxiv.1207.6246" @default.
- W4299527437 hasPublicationYear "2012" @default.
- W4299527437 type Work @default.
- W4299527437 citedByCount "0" @default.
- W4299527437 crossrefType "posted-content" @default.
- W4299527437 hasAuthorship W4299527437A5023940060 @default.
- W4299527437 hasAuthorship W4299527437A5037378898 @default.
- W4299527437 hasBestOaLocation W42995274371 @default.
- W4299527437 hasConcept C101837359 @default.
- W4299527437 hasConcept C105795698 @default.
- W4299527437 hasConcept C114614502 @default.
- W4299527437 hasConcept C118615104 @default.
- W4299527437 hasConcept C121332964 @default.
- W4299527437 hasConcept C121684516 @default.
- W4299527437 hasConcept C132525143 @default.
- W4299527437 hasConcept C134306372 @default.
- W4299527437 hasConcept C134786449 @default.
- W4299527437 hasConcept C151376022 @default.
- W4299527437 hasConcept C162307627 @default.
- W4299527437 hasConcept C197657726 @default.
- W4299527437 hasConcept C2776291640 @default.
- W4299527437 hasConcept C2779557605 @default.
- W4299527437 hasConcept C2779664074 @default.
- W4299527437 hasConcept C33923547 @default.
- W4299527437 hasConcept C41008148 @default.
- W4299527437 hasConcept C62520636 @default.
- W4299527437 hasConcept C76155785 @default.
- W4299527437 hasConceptScore W4299527437C101837359 @default.
- W4299527437 hasConceptScore W4299527437C105795698 @default.
- W4299527437 hasConceptScore W4299527437C114614502 @default.
- W4299527437 hasConceptScore W4299527437C118615104 @default.
- W4299527437 hasConceptScore W4299527437C121332964 @default.
- W4299527437 hasConceptScore W4299527437C121684516 @default.
- W4299527437 hasConceptScore W4299527437C132525143 @default.
- W4299527437 hasConceptScore W4299527437C134306372 @default.
- W4299527437 hasConceptScore W4299527437C134786449 @default.
- W4299527437 hasConceptScore W4299527437C151376022 @default.
- W4299527437 hasConceptScore W4299527437C162307627 @default.
- W4299527437 hasConceptScore W4299527437C197657726 @default.
- W4299527437 hasConceptScore W4299527437C2776291640 @default.
- W4299527437 hasConceptScore W4299527437C2779557605 @default.
- W4299527437 hasConceptScore W4299527437C2779664074 @default.
- W4299527437 hasConceptScore W4299527437C33923547 @default.
- W4299527437 hasConceptScore W4299527437C41008148 @default.
- W4299527437 hasConceptScore W4299527437C62520636 @default.
- W4299527437 hasConceptScore W4299527437C76155785 @default.
- W4299527437 hasLocation W42995274371 @default.
- W4299527437 hasLocation W42995274372 @default.
- W4299527437 hasOpenAccess W4299527437 @default.
- W4299527437 hasPrimaryLocation W42995274371 @default.
- W4299527437 hasRelatedWork W1963552444 @default.
- W4299527437 hasRelatedWork W2027879769 @default.
- W4299527437 hasRelatedWork W2039256426 @default.
- W4299527437 hasRelatedWork W2062644202 @default.
- W4299527437 hasRelatedWork W2080628395 @default.
- W4299527437 hasRelatedWork W3021340860 @default.
- W4299527437 hasRelatedWork W4205522560 @default.
- W4299527437 hasRelatedWork W4288357386 @default.
- W4299527437 hasRelatedWork W4319599984 @default.
- W4299527437 hasRelatedWork W264180933 @default.
- W4299527437 isParatext "false" @default.
- W4299527437 isRetracted "false" @default.
- W4299527437 workType "article" @default.