Computing and Combinatorics: 7th Annual International by Markus Bläser (auth.), Jie Wang (eds.)

By Markus Bläser (auth.), Jie Wang (eds.)

This publication constitutes the refereed lawsuits of the seventh Annual foreign convention on Computing and Combinatorics, COCOON 2001, held in Guilin, China, in August 2001.
The 50 revised complete papers and sixteen brief papers provided have been rigorously reviewed and chosen from ninety seven submissions. The papers are equipped in topical sections on complexity concept, computational biology, computational geometry, information constructions and algorithms, video games and combinatorics, graph algorithms and complexity, graph drawing, graph idea, on-line algorithms, randomized and average-case algorithms, Steiner bushes, platforms algorithms and modeling, and computability.

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Extra resources for Computing and Combinatorics: 7th Annual International Conference, COCOON 2001 Guilin, China, August 20–23, 2001 Proceedings

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One such example is the function which is computed by the BP that has a form of a complete binary tree and all the vertices read different variables. Separating Oblivious and Non-oblivious BPs 37 The final value is the value of the variable which is read at the end of each path. Clearly this function depends on all the variables and therefore any equivalent oblivious BP needs the depth which is equal to the number of variables. Such a separation is optimal due to Theorem 1. Our real purpose in this paper is not to give such a single example (which is enough only to prove a separation) but to give more general evidence that oblivious BPs need exponentially more depth than their non-oblivious counterparts for a wide range of Boolean functions.

3. F. Ablayev and M. Karpinski. “On the power of randomized branching programs ” Proc. 23th ICALP, LNCS 1099, 348-356, Paderbon, Germany, 8-12 July 1996. 4. N. Alon, and W. 410-417, 1986. 38 Kazuo Iwama, Yasuo Okabe, and Toshiro Takase 5. R. ” IEEE Trans. Computers, C-40(2), pp. 205-213, 1991. 6. L. Babai, N. Nisan, M. Szegedy, “Maltiparty protocols, pseudorandom generators for logspace, and time-space trade-offs” J. Computer System Sciences 45, pp. 204232, 1992. 7. A. Borodin, A. Razborov, R. Smolensky, “On lower-bounds for read-k-times branching programs” Computational Complexity, 3, pp.

As for lower-bounds on the depth of oblivious BPs, three Boolean functions have appeared in the literature: two have an Ω(N log N ) lower bound [4] and the third one has an Ω(N log2 N ) lower bound [6]. Our second function f2 is a modification of one of the two functions in [4]. Similar modification is also possible to the function in [6] and we can design an efficient syntactic BP. Unfortunately, we can only get an O(N ε ) upper bound for this syntactic depth at this moment (see Section 5). It is hard to cover all the related research in this detailed abstract.

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