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PolynomialTime Membership Comparable Sets
, 1994
"... This paper studies a notion called polynomialtime membership comparable sets. For a function g, a set A is polynomialtime gmembership comparable if there is a polynomialtime computable function f such that for any x 1 ; \Delta \Delta \Delta ; xm with m g(maxfjx 1 j; \Delta \Delta \Delta ; jx m j ..."
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Cited by 32 (5 self)
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membership comparable sets have polynomialsize circuits. 3. For any function f and for any constant c ? 0, if a set is p f(n)tt reducible to a Pselective set, then the set is polynomialtime (1 + c) log f(n)membership comparable. 4. For any C chosen from fPSPACE;UP;FewP;NP;C=P;PP;MOD 2 P; MOD 3 P
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
 Journal of the ACM
, 1998
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes ..."
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Cited by 397 (2 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
TimeSpace Lower Bounds for the PolynomialTime Hierarchy on Randomized Machines
 SIAM JOURNAL ON COMPUTING
, 2006
"... We establish the first polynomialstrength timespace lower bounds for problems in the lineartime hierarchy on randomized machines with twosided error. We show that for any integer ℓ> 1 and constant c < ℓ, there exists a positive constant d such that QSAT ℓ cannot be computed by such machine ..."
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Cited by 16 (5 self)
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We establish the first polynomialstrength timespace lower bounds for problems in the lineartime hierarchy on randomized machines with twosided error. We show that for any integer ℓ> 1 and constant c < ℓ, there exists a positive constant d such that QSAT ℓ cannot be computed
Polynomialtime construction of contraction hierarchies for multicriteria objectives
 In In Workshop on Algorithm Engineering and Experiments (ALENEX
"... In this paper we consider a variant of the multicriteria shortest path problem where the different criteria are combined in an arbitrary conic combination at query time. We show that contraction hierarchies (CH) a very powerful speedup technique originally developed for standard shortest path qu ..."
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Cited by 3 (0 self)
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traction operation during the CH construction can be performed in polynomialtime, while on the more practical side we complement our theoretical results with experiments on realworld data. Our approach extends previous results (Geisberger, Kobitzsch, and Sanders 2010) which only considered the bicriteria case
Polynomialtime multiselectivity
, 1997
"... We introduce a generalization of Selman's Pselectivity that yields a more flexible notion of selectivity, called (polynomialtime) multiselectivity, in which the selector is allowed to operate on multiple input strings. Since our introduction of this class, it has been used [HJRW96] to prove ..."
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Cited by 2 (1 self)
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and the properties of SH and completely establish, in terms of incomparability and strict inclusion, the relations between our generalized selectivity classes and Ogihara's Pmc (polynomialtime membershipcomparable) classes. Although SH is a strictly increasing infinite hierarchy, we show that the core
Notes on polynomialtime group theory
 CWI Quarterly
, 1992
"... Througbout. I.bis pap(!! ' h,t. C; (I') hn a subgrollp of 8 " generated by a subset l ' which may I)(! asslllllPd t() 1)() 'Slltal1 ' (Hay, of Hi~() < n2; d. Theorem 2.4iv). Tlw)1;o,tl will h( ' to (·OIll[Jlll.()]H·o])(!!'l.i(!s of c: '(1fliciellLly&ap ..."
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Cited by 1 (0 self)
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Througbout. I.bis pap(!! ' h,t. C; (I') hn a subgrollp of 8 " generated by a subset l ' which may I)(! asslllllPd t() 1)() 'Slltal1 ' (Hay, of Hi~() < n2; d. Theorem 2.4iv). Tlw)1;o,tl will h( ' to (·OIll[Jlll.()]H·o])(!!'l.i(!s of c: '(1fliciell
The Class NP Nondeterministic polynomialtime
"... A language L (equivalently decision problem) is in the class P if there is a polynomial time algorithm A for deciding L; Given a string x, A correctly decides if x ∈ L and running time of A on x is polynomial in x, the length of x. Given a contextfree grammar and a string, can that string be g ..."
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A language L (equivalently decision problem) is in the class P if there is a polynomial time algorithm A for deciding L; Given a string x, A correctly decides if x ∈ L and running time of A on x is polynomial in x, the length of x. Given a contextfree grammar and a string, can that string
An Implicit Characterization of the PolynomialTime Decidable Sets by ConsFree Rewriting
"... Abstract. We define the class of constrained consfree rewriting systems and show that this class characterizes P, the set of languages decidable in polynomial time on a deterministic Turing machine. The main novelty of the characterization is that it allows very liberal properties of term rewritin ..."
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Abstract. We define the class of constrained consfree rewriting systems and show that this class characterizes P, the set of languages decidable in polynomial time on a deterministic Turing machine. The main novelty of the characterization is that it allows very liberal properties of term
Results 1  10
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293,217