By Markus Bläser (auth.), Jie Wang (eds.)
This ebook constitutes the refereed court cases 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 awarded have been conscientiously reviewed and chosen from ninety seven submissions. The papers are equipped in topical sections on complexity conception, computational biology, computational geometry, facts buildings and algorithms, video games and combinatorics, graph algorithms and complexity, graph drawing, graph conception, on-line algorithms, randomized and average-case algorithms, Steiner bushes, platforms algorithms and modeling, and computability.
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Extra info for Computing and Combinatorics: 7th Annual International Conference, COCOON 2001 Guilin, China, August 20–23, 2001 Proceedings
Theorem 6. No co-sparse language in P is universally simplifying. 26 Nicholas Tran Proof. Let L ∈ P be a language whose complement is sparse. Deﬁne a polynomialtime 1-1 function f : Σ ∗ → L as follows: on input w, f searches for the lexicographically ﬁrst string v of length |w|, such that vw ∈ L and outputs vw. Such a string exists and can be found in polynomial time since L is in P and L is sparse. Clearly f is one-one. For any NP-complete language C, its image f (C) ⊆ L is also in NP, since f is polynomially honest, and therefore NP-complete.
Xm } are known as the input-output variables, with the remaining variables being the free variables. The remaining instructions are one of the following: an assignment instruction of the form ‘xi := y’, where y is a variable or a constant symbol; a guess instruction of the form ‘guess xi ’; a while instruction of the form ‘while ϕ do α1 ; α2 ; . . ; αq od’, where ϕ is a quantiﬁer-free ﬁrst-order formula over σ and where each of α1 , α2 , . . , αq is another instruction of one of the forms given here; or an accept instruction accept or a reject instruction reject.
Discrete Appl. : SL ⊆ L4/3 . : Bounds on universal sequences. SIAM J. Comput. 18(2) (1989) 268–277 [B] Bridgland, M. : Universal traversal sequences for paths and cycles. J. : Lower bounds on universal traversal sequences based on chains of length ﬁve. Inf. and Comp. : Universal traversal sequences for expander graphs. Inf. Proc. : Polynomial universal traversing sequences for cycles are constructible (extended abstract). Proceedings of 20-th STOC (1988) 491–503 [KPS] Karloﬀ, H. : Universal traversal sequences of length nO(logn) for cliques.