{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article11305","name":"Near-Optimal Distance Emulator for Planar Graphs","abstract":"Given a graph G and a set of terminals T, a distance emulator of G is another graph H (not necessarily a subgraph of G) containing T, such that all the pairwise distances in G between vertices of T are preserved in H. An important open question is to find the smallest possible distance emulator.\nWe prove that, given any subset of k terminals in an n-vertex undirected unweighted planar graph, we can construct in O~(n) time a distance emulator of size O~(min(k^2,sqrt{k * n})). This is optimal up to logarithmic factors. The existence of such distance emulator provides a straightforward framework to solve distance-related problems on planar graphs: Replace the input graph with the distance emulator, and apply whatever algorithm available to the resulting emulator. In particular, our result implies that, on any unweighted undirected planar graph, one can compute all-pairs shortest path distances among k terminals in O~(n) time when k=O(n^{1\/3}).","keywords":["planar graphs","shortest paths","metric compression","distance preservers","distance emulators","distance oracles"],"author":[{"@type":"Person","name":"Chang, Hsien-Chih","givenName":"Hsien-Chih","familyName":"Chang","affiliation":"University of Illinois at Urbana-Champaign, USA","funding":"Supported partially by NSF grant CCF-1408763."},{"@type":"Person","name":"Gawrychowski, Pawel","givenName":"Pawel","familyName":"Gawrychowski","affiliation":"University of Wroc\u0142aw, Poland"},{"@type":"Person","name":"Mozes, Shay","givenName":"Shay","familyName":"Mozes","affiliation":"IDC Herzliya, Israel","funding":"Supported partially by ISF grants 794\/13 and 592\/17"},{"@type":"Person","name":"Weimann, Oren","givenName":"Oren","familyName":"Weimann","affiliation":"University of Haifa, Israel","funding":"Supported partially by ISF grants 794\/13 and 592\/17"}],"position":16,"pageStart":"16:1","pageEnd":"16:17","dateCreated":"2018-08-14","datePublished":"2018-08-14","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Chang, Hsien-Chih","givenName":"Hsien-Chih","familyName":"Chang","affiliation":"University of Illinois at Urbana-Champaign, USA","funding":"Supported partially by NSF grant CCF-1408763."},{"@type":"Person","name":"Gawrychowski, Pawel","givenName":"Pawel","familyName":"Gawrychowski","affiliation":"University of Wroc\u0142aw, Poland"},{"@type":"Person","name":"Mozes, Shay","givenName":"Shay","familyName":"Mozes","affiliation":"IDC Herzliya, Israel","funding":"Supported partially by ISF grants 794\/13 and 592\/17"},{"@type":"Person","name":"Weimann, Oren","givenName":"Oren","familyName":"Weimann","affiliation":"University of Haifa, Israel","funding":"Supported partially by ISF grants 794\/13 and 592\/17"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ESA.2018.16","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6315","volumeNumber":112,"name":"26th Annual European Symposium on Algorithms (ESA 2018)","dateCreated":"2018-08-14","datePublished":"2018-08-14","editor":[{"@type":"Person","name":"Azar, Yossi","givenName":"Yossi","familyName":"Azar"},{"@type":"Person","name":"Bast, Hannah","givenName":"Hannah","familyName":"Bast"},{"@type":"Person","name":"Herman, Grzegorz","givenName":"Grzegorz","familyName":"Herman"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article11305","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6315"}}}