{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article11579","name":"Maximum Rooted Connected Expansion","abstract":"Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As a result, estimating the amount of resources that need to be preloaded during a surfer's browsing becomes an important task. In this regard, prefetching can be modeled as a two-player combinatorial game [Fomin et al., Theoretical Computer Science 2014], where a surfer and a marker alternately play on a given graph (representing the Web graph). During its turn, the marker chooses a set of k nodes to mark (prefetch), whereas the surfer, represented as a token resting on graph nodes, moves to a neighboring node (Web resource). The surfer's objective is to reach an unmarked node before all nodes become marked and the marker wins. Intuitively, since the surfer is step-by-step traversing a subset of nodes in the Web graph, a satisfactory prefetching procedure would load in cache (without any delay) all resources lying in the neighborhood of this growing subset.\nMotivated by the above, we consider the following maximization problem to which we refer to as the Maximum Rooted Connected Expansion (MRCE) problem. Given a graph G and a root node v_0, we wish to find a subset of vertices S such that S is connected, S contains v_0 and the ratio |N[S]|\/|S| is maximized, where N[S] denotes the closed neighborhood of S, that is, N[S] contains all nodes in S and all nodes with at least one neighbor in S.\nWe prove that the problem is NP-hard even when the input graph G is restricted to be a split graph. On the positive side, we demonstrate a polynomial time approximation scheme for split graphs. Furthermore, we present a 1\/6(1-1\/e)-approximation algorithm for general graphs based on techniques for the Budgeted Connected Domination problem [Khuller et al., SODA 2014]. Finally, we provide a polynomial-time algorithm for the special case of interval graphs. Our algorithm returns an optimal solution for MRCE in O(n^3) time, where n is the number of nodes in G.","keywords":["prefetching","domination","expansion","ratio"],"author":[{"@type":"Person","name":"Lamprou, Ioannis","givenName":"Ioannis","familyName":"Lamprou","affiliation":"Department of Computer Science, University of Liverpool, Liverpool, UK"},{"@type":"Person","name":"Martin, Russell","givenName":"Russell","familyName":"Martin","affiliation":"Department of Computer Science, University of Liverpool, Liverpool, UK"},{"@type":"Person","name":"Schewe, Sven","givenName":"Sven","familyName":"Schewe","affiliation":"Department of Computer Science, University of Liverpool, Liverpool, UK"},{"@type":"Person","name":"Sigalas, Ioannis","givenName":"Ioannis","familyName":"Sigalas","affiliation":"Department of Informatics & Telecommunications, University of Athens, Athens, Greece"},{"@type":"Person","name":"Zissimopoulos, Vassilis","givenName":"Vassilis","familyName":"Zissimopoulos","affiliation":"Department of Informatics & Telecommunications, University of Athens, Athens, Greece"}],"position":25,"pageStart":"25:1","pageEnd":"25:14","dateCreated":"2018-08-27","datePublished":"2018-08-27","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Lamprou, Ioannis","givenName":"Ioannis","familyName":"Lamprou","affiliation":"Department of Computer Science, University of Liverpool, Liverpool, UK"},{"@type":"Person","name":"Martin, Russell","givenName":"Russell","familyName":"Martin","affiliation":"Department of Computer Science, University of Liverpool, Liverpool, UK"},{"@type":"Person","name":"Schewe, Sven","givenName":"Sven","familyName":"Schewe","affiliation":"Department of Computer Science, University of Liverpool, Liverpool, UK"},{"@type":"Person","name":"Sigalas, Ioannis","givenName":"Ioannis","familyName":"Sigalas","affiliation":"Department of Informatics & Telecommunications, University of Athens, Athens, Greece"},{"@type":"Person","name":"Zissimopoulos, Vassilis","givenName":"Vassilis","familyName":"Zissimopoulos","affiliation":"Department of Informatics & Telecommunications, University of Athens, Athens, Greece"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.MFCS.2018.25","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":"https:\/\/www.w3.org\/TR\/resource-hints\/","isPartOf":{"@type":"PublicationVolume","@id":"#volume6320","volumeNumber":117,"name":"43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)","dateCreated":"2018-08-27","datePublished":"2018-08-27","editor":[{"@type":"Person","name":"Potapov, Igor","givenName":"Igor","familyName":"Potapov"},{"@type":"Person","name":"Spirakis, Paul","givenName":"Paul","familyName":"Spirakis"},{"@type":"Person","name":"Worrell, James","givenName":"James","familyName":"Worrell"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article11579","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":"#volume6320"}}}