Matches in SemOpenAlex for { <https://semopenalex.org/work/W4385961300> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4385961300 abstract "The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices $u$ and $v$ in the graph, there exists a path between $u$ and $v$ that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch $1+varepsilon$ and $O(1)$ many trees for any fixed $varepsilon in (0,1)$. However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the planarity barrier to construct a shortcut partition for $K_r$-minor-free graphs for any $r$. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for $K_r$-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for $K_r$-minor-free graphs, with $1+varepsilon$ stretch, linear space, and constant query time for any fixed $varepsilon in (0,1)$. The previous best distance oracle [AG06] uses $O(nlog n)$ space and $O(log n)$ query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of $O(1)$ size for minor-free graphs with stretch $1+varepsilon$, while the previous best $(1+varepsilon)$-tree cover has size $O(log^2 n)$ [BFN19]." @default.
- W4385961300 created "2023-08-18" @default.
- W4385961300 creator A5003923315 @default.
- W4385961300 creator A5050147589 @default.
- W4385961300 creator A5054075729 @default.
- W4385961300 creator A5067955248 @default.
- W4385961300 creator A5078515449 @default.
- W4385961300 creator A5084685735 @default.
- W4385961300 date "2023-07-31" @default.
- W4385961300 modified "2023-10-16" @default.
- W4385961300 title "Shortcut Partitions in Minor-Free Graphs: Steiner Point Removal, Distance Oracles, Tree Covers, and More" @default.
- W4385961300 doi "https://doi.org/10.48550/arxiv.2308.00555" @default.
- W4385961300 hasPublicationYear "2023" @default.
- W4385961300 type Work @default.
- W4385961300 citedByCount "0" @default.
- W4385961300 crossrefType "posted-content" @default.
- W4385961300 hasAuthorship W4385961300A5003923315 @default.
- W4385961300 hasAuthorship W4385961300A5050147589 @default.
- W4385961300 hasAuthorship W4385961300A5054075729 @default.
- W4385961300 hasAuthorship W4385961300A5067955248 @default.
- W4385961300 hasAuthorship W4385961300A5078515449 @default.
- W4385961300 hasAuthorship W4385961300A5084685735 @default.
- W4385961300 hasBestOaLocation W43859613001 @default.
- W4385961300 hasConcept C101837359 @default.
- W4385961300 hasConcept C114614502 @default.
- W4385961300 hasConcept C118615104 @default.
- W4385961300 hasConcept C132525143 @default.
- W4385961300 hasConcept C17744445 @default.
- W4385961300 hasConcept C199539241 @default.
- W4385961300 hasConcept C2779760435 @default.
- W4385961300 hasConcept C33923547 @default.
- W4385961300 hasConcept C42812 @default.
- W4385961300 hasConcept C68260962 @default.
- W4385961300 hasConcept C76220878 @default.
- W4385961300 hasConceptScore W4385961300C101837359 @default.
- W4385961300 hasConceptScore W4385961300C114614502 @default.
- W4385961300 hasConceptScore W4385961300C118615104 @default.
- W4385961300 hasConceptScore W4385961300C132525143 @default.
- W4385961300 hasConceptScore W4385961300C17744445 @default.
- W4385961300 hasConceptScore W4385961300C199539241 @default.
- W4385961300 hasConceptScore W4385961300C2779760435 @default.
- W4385961300 hasConceptScore W4385961300C33923547 @default.
- W4385961300 hasConceptScore W4385961300C42812 @default.
- W4385961300 hasConceptScore W4385961300C68260962 @default.
- W4385961300 hasConceptScore W4385961300C76220878 @default.
- W4385961300 hasLocation W43859613001 @default.
- W4385961300 hasOpenAccess W4385961300 @default.
- W4385961300 hasPrimaryLocation W43859613001 @default.
- W4385961300 hasRelatedWork W137798462 @default.
- W4385961300 hasRelatedWork W2058555041 @default.
- W4385961300 hasRelatedWork W2088919915 @default.
- W4385961300 hasRelatedWork W2289086174 @default.
- W4385961300 hasRelatedWork W3043321318 @default.
- W4385961300 hasRelatedWork W4295995756 @default.
- W4385961300 hasRelatedWork W4305006088 @default.
- W4385961300 hasRelatedWork W4308445215 @default.
- W4385961300 hasRelatedWork W4313482007 @default.
- W4385961300 hasRelatedWork W4364296635 @default.
- W4385961300 isParatext "false" @default.
- W4385961300 isRetracted "false" @default.
- W4385961300 workType "article" @default.