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

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

This booklet constitutes the refereed court cases of the seventh Annual overseas convention on Computing and Combinatorics, COCOON 2001, held in Guilin, China, in August 2001.
The 50 revised complete papers and sixteen brief papers offered have been rigorously reviewed and chosen from ninety seven submissions. The papers are equipped in topical sections on complexity conception, computational biology, computational geometry, information buildings and algorithms, video games and combinatorics, graph algorithms and complexity, graph drawing, graph concept, on-line algorithms, randomized and average-case algorithms, Steiner timber, structures algorithms and modeling, and computability.

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

Sample text

Again, the classes of structures accepted by the program schemes of NPSQ+ (1) are problems. , as a bit-string. Nevertheless, we can still arrange for finite structures to be input to Turing machines by encoding them as strings (throughout, our Turing machines are non-deterministic). We say that a problem Ω over σ is accepted by a Turing machine M if M accepts exactly those bit-strings encoding structures in Ω; and so, in particular, as to whether an encoding eσ (A) of any σ-structure A is accepted by M is independent of the particular linear order of the elements chosen when encoding A.

These two types of languages together are called universally easy languages. It turns out that C, the set of chordal graphs, is not a universally simplifying language, since the graph-theoretic problem of λ-COLORING remains NP-complete for chordal graphs [3]. Assuming that P = NP, it follows that C is not universally polynomial. This research is partially supported by an SCU-IBM Faculty Research Grant. J. ): COCOON 2001, LNCS 2108, pp. 21–27, 2001. c Springer-Verlag Berlin Heidelberg 2001 22 Nicholas Tran It is easy to see that all finite languages are universally polynomial.

Select arbitrary 2ε log N Z-variables in βi and let BZi be the set of those variables. Also let BZi be the set of the remaining (1 − 2ε ) log N variables in βi . Recall that the value assigned to βi variables is a pointer to some variable xi (1 ≤ i ≤ N ). Hence we can define the following equivalence classes on the set of the whole N variables: Ej = {xi | the pointer to xi (= the value i) has the same 0/1 assignments (= j) to BZi variables } ε ε Note that the number of these equivalence classes is 2(1− 2 ) log N = N 1− 2 , ε ε ε 2N 2 A-variables or more.

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