NDLI: An Efficient Algorithm for Partial Order Production

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Cardinal, Jean Jungers, Raphal M. Fiorini, Samuel Munro, J. Ian Joret, Gwenal
Copyright Year	2010
Abstract	We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S by comparing a minimum number of pairs in T. Special cases include sorting by comparisons, selection, multiple selection, and heap construction. We give an algorithm performing $ITLB+o(ITLB)+O(n)$ comparisons in the worst case. Here, n denotes the size of the ground sets, and $ITLB$ denotes a natural information-theoretic lower bound on the number of comparisons needed to produce the target partial order. Our approach is to replace the target partial order by a weak order (that is, a partial order with a layered structure) extending it, without increasing the information-theoretic lower bound too much. We then solve the problem by applying an efficient multiple selection algorithm. The overall complexity of our algorithm is polynomial. This answers a question of Yao [SIAM J. Comput., 18 (1989), pp. 679689]. We base our analysis on the entropy of the target partial order, a quantity that can be efficiently computed and provides a good estimate of the information-theoretic lower bound.
Starting Page	2927
Ending Page	2940
Page Count	14
File Format	PDF
ISSN	00975397
DOI	10.1137/090759860
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	7
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-05-05
Access Restriction	Subscribed
Subject Keyword	Analysis of algorithms and problem complexity Partial order, general Dominating sets, independent sets, cliques Searching and sorting Graph algorithms Perfect graphs Combinatorial optimization partial order graph entropy Programming involving graphs or networks
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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