Models of random partial orders
Surveys in combinatorics, 1993
The average number of linear extensions of a partial order
Journal of Combinatorial Theory Series A
The Structure of Random Graph Orders
SIAM Journal on Discrete Mathematics
SIAM Journal on Computing
On tail distribution of interpost distance
Journal of Combinatorial Theory Series B
Phase transitions in the evolution of partial orders
Journal of Combinatorial Theory Series A
Counting Partial Orders with a Fixed Number of Comparable Pairs
Combinatorics, Probability and Computing
Minimum average cost testing for partially ordered components
IEEE Transactions on Information Theory
An efficient search algorithm for partially ordered sets
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
On searching a table consistent with division poset
Theoretical Computer Science
Finding an optimal tree searching strategy in linear time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Optimal Binary Decision Trees
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
On the complexity of searching in trees: average-case minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the Huffman and alphabetic tree problem with general cost functions
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Searching in dynamic tree-like partial orders
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
On the complexity of searching in trees and partially ordered structures
Theoretical Computer Science
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We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing efficiently near-optimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform model.We shall show that the problem of determining an optimal strategy is NP-hard, but there are simple, fast algorithms able to produce near-optimal search strategies for typical partial orders under the two models of random partial orders that we consider. We present a (1 + o(1))- approximation algorithm for typical partial orders under the random graph model (constant p) and present a 6.34-approximation algorithm for typical partial orders under the uniform model. Both algorithms run in polynomial time.