{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article11082","name":"Generic Single Edge Fault Tolerant Exact Distance Oracle","abstract":"Given an undirected unweighted graph G and a source set S of |S| = sigma sources, we want to build a data structure which can process the following query Q(s,t,e): find the shortest distance from s to t avoiding an edge e, where s in S and t in V. When sigma=n, Demetrescu, Thorup, Chowdhury and Ramachandran (SIAM Journal of Computing, 2008) designed an algorithm with O~(n^2) space and O(1) query time. A natural open question is to generalize this result to any number of sources. Recently, Bil{\u00f2} et. al. (STACS 2018) designed a data-structure of size O~(sigma^{1\/2}n^{3\/2}) with the query time of O(sqrt{n sigma}) for the above problem. We improve their result by designing a data-structure of size O~(sigma^{1\/2} n^{3\/2}) that can answer queries in O~(1) time.\nIn a related problem of finding fault tolerant subgraph, Parter and Peleg (ESA 2013) showed that if detours of replacement paths ending at a vertex t are disjoint, then the number of such paths is O(sqrt{n sigma}). This eventually gives a bound of O(n sqrt{n sigma}) = O(sigma^{1\/2}n^{3\/2}) for their problem. Disjointness of detours is a very crucial property used in the above result. We show a similar result for a subset of replacement path which may not be disjoint. This result is the crux of our paper and may be of independent interest.","keywords":["Fault Tolerant Algorithms","Graph Algorithms","Distance Oracles","Data-Structures"],"author":[{"@type":"Person","name":"Gupta, Manoj","givenName":"Manoj","familyName":"Gupta","affiliation":"IIT Gandhinagar, Gandhinagar, India"},{"@type":"Person","name":"Singh, Aditi","givenName":"Aditi","familyName":"Singh","affiliation":"IIT Gandhinagar, Gandhinagar, India"}],"position":72,"pageStart":"72:1","pageEnd":"72:15","dateCreated":"2018-07-04","datePublished":"2018-07-04","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Gupta, Manoj","givenName":"Manoj","familyName":"Gupta","affiliation":"IIT Gandhinagar, Gandhinagar, India"},{"@type":"Person","name":"Singh, Aditi","givenName":"Aditi","familyName":"Singh","affiliation":"IIT Gandhinagar, Gandhinagar, India"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2018.72","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6310","volumeNumber":107,"name":"45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)","dateCreated":"2018-07-04","datePublished":"2018-07-04","editor":[{"@type":"Person","name":"Chatzigiannakis, Ioannis","givenName":"Ioannis","familyName":"Chatzigiannakis"},{"@type":"Person","name":"Kaklamanis, Christos","givenName":"Christos","familyName":"Kaklamanis"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"},{"@type":"Person","name":"Sannella, Donald","givenName":"Donald","familyName":"Sannella"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article11082","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":"#volume6310"}}}