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- W2963319367 abstract "Given a graph where vertices are partitioned into k terminals and non-terminals, the goal is to compress the graph (i.e., reduce the number of non-terminals) using minor operations while preserving terminal distances approximately. The distortion of a compressed graph is the maximum multiplicative blow-up of distances between all pairs of terminals. We study the trade-off between the number of non-terminals and the distortion. This problem generalizes the Steiner Point Removal (SPR) problem, in which all non-terminals must be removed.We introduce a novel black-box reduction to convert any lower bound on distortion for the SPR problem into a super-linear lower bound on the number of non-terminals, with the same distortion, for our problem. This allows us to show that there exist graphs such that every minor with distortion less than 2 / 2.5 / 3 must have Omega(k^2) / Omega(k^{5/4}) / Omega(k^{6/5}) non-terminals, plus more trade-offs in between. The black-box reduction has an interesting consequence: if the tight lower bound on distortion for the SPR problem is super-constant, then allowing any O(k) non-terminals will not help improving the lower bound to a constant.We also build on the existing results on spanners, distance oracles and connected 0-extensions to show a number of upper bounds for general graphs, planar graphs, graphs that exclude a fixed minor and bounded treewidth graphs. Among others, we show that any graph admits a minor with O(log k) distortion and O(k^2) non-terminals, and any planar graph admits a minor with1 + epsilon distortion and ~O((k/epsilon)^2) non-terminals." @default.
- W2963319367 created "2019-07-30" @default.
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- W2963319367 date "2016-04-01" @default.
- W2963319367 modified "2023-10-07" @default.
- W2963319367 title "Graph Minors for Preserving Terminal Distances Approximately - Lower and Upper Bounds." @default.
- W2963319367 doi "https://doi.org/10.4230/lipics.icalp.2016.131" @default.
- W2963319367 hasPublicationYear "2016" @default.
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