Browsing by Subject "Lower bounds"

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  • Korhonen, J.H.; Rybicki, J. (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
    Leibniz International Proceedings in Informatics (LIPIcs)
    We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: For any constant k, detecting k-paths and trees on k nodes can be done in O(1) rounds. For any constant k, detecting k-cycles and pseudotrees on k nodes can be done in O(n) rounds. On d-degenerate graphs, cliques and 4-cycles can be enumerated in O(d+log n) rounds, and 5-cycles in O(d2 + log n) rounds. In many cases, these bounds are tight up to logarithmic factors. Moreover, we show that the algorithms for d-degenerate graphs can be improved to O(d/ log n) and O(d2/log n), respectively, in the supported CONGEST model, which can be seen as an intermediate model between CONGEST and the congested clique. © 2017 Janne H. Korhonen and Joel Rybicki.
  • Kosolobov, Dmitry (2017)
    The longest common extension problem is to preprocess a given string of length n into a data structure that uses S(n) bits on top of the input and answers in T(n) time the queries LCE(i, j) computing the length of the longest string that occurs at both positions i and j in the input. We prove that the trade-off S (n)T (n) = (it logn) holds in the non-uniform cell-probe model provided that the input string is read-only, each letter occupies a separate memory cell, S(n) = Omega(n), and the size of the input alphabet is at least 2(8inverted right perpendicularS(n)/ninverted left perpendicular). It is known that this trade-off is tight. (C) 2017 Elsevier B.V. All rights reserved.