Fast algorithms for constructing maximum entropy summary trees

Richard Cole, Howard Karloff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Karloff and Shirley recently proposed "summary trees" as a new way to visualize large rooted trees (Eurovis 2013) and gave algorithms for generating a maximum-entropy k-node summary tree of an input n-node rooted tree. However, the algorithm generating optimal summary trees was only pseudo-polynomial (and worked only for integral weights); the authors left open existence of a polynomial-time algorithm. In addition, the authors provided an additive approximation algorithm and a greedy heuristic, both working on real weights. This paper shows how to construct maximum entropy k-node summary trees in time O(k2 n + n log n) for real weights (indeed, as small as the time bound for the greedy heuristic given previously); how to speed up the approximation algorithm so that it runs in time O(n + (k4/ε) log(k/ε)), and how to speed up the greedy algorithm so as to run in time O(kn + n log n). Altogether, these results make summary trees a much more practical tool than before.

Original languageEnglish (US)
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Pages332-343
Number of pages12
Volume8572 LNCS
EditionPART 1
ISBN (Print)9783662439470
DOIs
StatePublished - 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: Jul 8 2014Jul 11 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
CountryDenmark
CityCopenhagen
Period7/8/147/11/14

Fingerprint

Maximum Entropy
Fast Algorithm
Entropy
Approximation algorithms
Greedy Heuristics
Rooted Trees
Polynomials
Approximation Algorithms
Speedup
Vertex of a graph
Trees (mathematics)
Greedy Algorithm
Polynomial-time Algorithm
Polynomial

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Cole, R., & Karloff, H. (2014). Fast algorithms for constructing maximum entropy summary trees. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings (PART 1 ed., Vol. 8572 LNCS, pp. 332-343). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_28

Fast algorithms for constructing maximum entropy summary trees. / Cole, Richard; Karloff, Howard.

Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings. Vol. 8572 LNCS PART 1. ed. Springer Verlag, 2014. p. 332-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cole, R & Karloff, H 2014, Fast algorithms for constructing maximum entropy summary trees. in Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings. PART 1 edn, vol. 8572 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 8572 LNCS, Springer Verlag, pp. 332-343, 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014, Copenhagen, Denmark, 7/8/14. https://doi.org/10.1007/978-3-662-43948-7_28
Cole R, Karloff H. Fast algorithms for constructing maximum entropy summary trees. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings. PART 1 ed. Vol. 8572 LNCS. Springer Verlag. 2014. p. 332-343. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-662-43948-7_28
Cole, Richard ; Karloff, Howard. / Fast algorithms for constructing maximum entropy summary trees. Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings. Vol. 8572 LNCS PART 1. ed. Springer Verlag, 2014. pp. 332-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
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