Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952487150> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W2952487150 abstract "This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {it minimum normalized cuts}/{it isoperimteric numbers} defined through taking minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a {it partition}/{it subpartition}. Following the main result of [A. Daneshgar, {it et. al.}, {it On the isoperimetric spectrum of graphs and its approximations}, JCTB, (2010)], it is known that the isoperimetric number and the minimum normalized cut both can be described as ${0,1}$-optimization programs, where the latter one does {it not} admit a relaxation to the reals. We show that the decision problem for the case of taking $k$-partitions and the maximum (called the max normalized cut problem {rm NCP}$^M$) as well as the other two decision problems for the mean version (referred to as {rm IPP}$^m$ and {rm NCP}$^m$) are $NP$-complete problems. On the other hand, we show that the decision problem for the case of taking $k$-subpartitions and the maximum (called the max isoperimetric problem {rm IPP}$^M$) can be solved in {it linear time} for any weighted tree and any $k geq 2$. Based on this fact, we provide polynomial time $O(k)$-approximation algorithms for all different versions of $k$th isoperimetric numbers considered. Moreover, when the number of partitions/subpartitions, $k$, is a fixed constant, as an extension of a result of B. Mohar (1989) for the case $k=2$ (usually referred to as the Cheeger constant), we prove that max and mean isoperimetric numbers of weighted trees as well as their max normalized cut can be computed in polynomial time. We also prove some hardness results for the case of simple unweighted graphs and trees." @default.
- W2952487150 created "2019-06-27" @default.
- W2952487150 creator A5013062876 @default.
- W2952487150 creator A5066820962 @default.
- W2952487150 date "2010-09-03" @default.
- W2952487150 modified "2023-09-27" @default.
- W2952487150 title "On Complexity of Isoperimetric Problems on Trees" @default.
- W2952487150 cites W1505597232 @default.
- W2952487150 cites W1586726865 @default.
- W2952487150 cites W1973138963 @default.
- W2952487150 cites W2011039300 @default.
- W2952487150 cites W2027199101 @default.
- W2952487150 cites W2030724586 @default.
- W2952487150 cites W2063488705 @default.
- W2952487150 cites W2090987888 @default.
- W2952487150 cites W2091603956 @default.
- W2952487150 cites W2105630880 @default.
- W2952487150 cites W2121947440 @default.
- W2952487150 cites W2138300049 @default.
- W2952487150 cites W2166435158 @default.
- W2952487150 cites W2279278398 @default.
- W2952487150 cites W2611804663 @default.
- W2952487150 cites W2949598044 @default.
- W2952487150 hasPublicationYear "2010" @default.
- W2952487150 type Work @default.
- W2952487150 sameAs 2952487150 @default.
- W2952487150 citedByCount "0" @default.
- W2952487150 crossrefType "posted-content" @default.
- W2952487150 hasAuthorship W2952487150A5013062876 @default.
- W2952487150 hasAuthorship W2952487150A5066820962 @default.
- W2952487150 hasConcept C11413529 @default.
- W2952487150 hasConcept C114614502 @default.
- W2952487150 hasConcept C115988155 @default.
- W2952487150 hasConcept C118615104 @default.
- W2952487150 hasConcept C140142295 @default.
- W2952487150 hasConcept C15744967 @default.
- W2952487150 hasConcept C199360897 @default.
- W2952487150 hasConcept C2776029896 @default.
- W2952487150 hasConcept C2777027219 @default.
- W2952487150 hasConcept C311688 @default.
- W2952487150 hasConcept C33923547 @default.
- W2952487150 hasConcept C41008148 @default.
- W2952487150 hasConcept C42812 @default.
- W2952487150 hasConcept C77805123 @default.
- W2952487150 hasConceptScore W2952487150C11413529 @default.
- W2952487150 hasConceptScore W2952487150C114614502 @default.
- W2952487150 hasConceptScore W2952487150C115988155 @default.
- W2952487150 hasConceptScore W2952487150C118615104 @default.
- W2952487150 hasConceptScore W2952487150C140142295 @default.
- W2952487150 hasConceptScore W2952487150C15744967 @default.
- W2952487150 hasConceptScore W2952487150C199360897 @default.
- W2952487150 hasConceptScore W2952487150C2776029896 @default.
- W2952487150 hasConceptScore W2952487150C2777027219 @default.
- W2952487150 hasConceptScore W2952487150C311688 @default.
- W2952487150 hasConceptScore W2952487150C33923547 @default.
- W2952487150 hasConceptScore W2952487150C41008148 @default.
- W2952487150 hasConceptScore W2952487150C42812 @default.
- W2952487150 hasConceptScore W2952487150C77805123 @default.
- W2952487150 hasLocation W29524871501 @default.
- W2952487150 hasOpenAccess W2952487150 @default.
- W2952487150 hasPrimaryLocation W29524871501 @default.
- W2952487150 hasRelatedWork W1506627918 @default.
- W2952487150 hasRelatedWork W1609018602 @default.
- W2952487150 hasRelatedWork W1824295098 @default.
- W2952487150 hasRelatedWork W1944873932 @default.
- W2952487150 hasRelatedWork W1956536100 @default.
- W2952487150 hasRelatedWork W1988547891 @default.
- W2952487150 hasRelatedWork W2100048208 @default.
- W2952487150 hasRelatedWork W2170054126 @default.
- W2952487150 hasRelatedWork W2179340953 @default.
- W2952487150 hasRelatedWork W2220764785 @default.
- W2952487150 hasRelatedWork W2272158670 @default.
- W2952487150 hasRelatedWork W2285165722 @default.
- W2952487150 hasRelatedWork W2392378295 @default.
- W2952487150 hasRelatedWork W2953048456 @default.
- W2952487150 hasRelatedWork W3001868306 @default.
- W2952487150 hasRelatedWork W3098071389 @default.
- W2952487150 hasRelatedWork W3160700943 @default.
- W2952487150 hasRelatedWork W3184813271 @default.
- W2952487150 hasRelatedWork W3196006997 @default.
- W2952487150 hasRelatedWork W2123734400 @default.
- W2952487150 isParatext "false" @default.
- W2952487150 isRetracted "false" @default.
- W2952487150 magId "2952487150" @default.
- W2952487150 workType "article" @default.