共查询到20条相似文献,搜索用时 639 毫秒
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We prove an explicit bound on the radius of a ball centered at the origin which is guaranteed to contain all bounded connected components of a semi-algebraic set S⊂Rk defined by a weak sign condition involving s polynomials in Z[X1,…,Xk] having degrees at most d, and whose coefficients have bitsizes at most τ. Our bound is an explicit function of s,d,k and τ, and does not contain any undetermined constants. We also prove a similar bound on the radius of a ball guaranteed to intersect every connected component of S (including the unbounded components). While asymptotic bounds of the form 2τdO(k) on these quantities were known before, some applications require bounds which are explicit and which hold for all values of s,d,k and τ. The bounds proved in this paper are of this nature. 相似文献
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We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex. 相似文献
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A collection of T1,T2,…,Tk of unrooted, leaf labelled (phylogenetic) trees, all with different leaf sets, is said to be compatible if there exists a tree T such that each tree Ti can be obtained from T by deleting leaves and contracting edges. Determining compatibility is NP-hard, and the fastest algorithm to date has worst case complexity of around Ω(nk) time, n being the number of leaves. Here, we present an O(nf(k)) algorithm, proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable (FPT) with respect to the number k of trees. 相似文献
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Taisuke Izumi Akinori Saitoh Toshimitsu Masuzawa 《Journal of Parallel and Distributed Computing》2007
The Δ-timed uniform consensus is a stronger variant of the traditional consensus and it satisfies the following additional property: every correct process terminates its execution within a constant time Δ (Δ-timeliness), and no two processes decide differently (uniformity). In this paper, we consider the Δ-timed uniform consensus problem in presence of fc crash processes and ft timing-faulty processes, and propose a Δ-timed uniform consensus algorithm. The proposed algorithm is adaptive in the following sense: it solves the Δ-timed uniform consensus when at least ft+1 correct processes exist in the system. If the system has less than ft+1 correct processes, the algorithm cannot solve the Δ-timed uniform consensus. However, as long as ft+1 processes are non-crashed, the algorithm solves (non-timed) uniform consensus. We also investigate the maximum number of faulty processes that can be tolerated. We show that any Δ-timed uniform consensus algorithm tolerating up to ft timing-faulty processes requires that the system has at least ft+1 correct processes. This impossibility result implies that the proposed algorithm attains the maximum resilience about the number of faulty processes. We also show that any Δ-timed uniform consensus algorithm tolerating up to ft timing-faulty processes cannot solve the (non-timed) uniform consensus when the system has less than ft+1 non-crashed processes. This impossibility result implies that our algorithm attains the maximum adaptiveness. 相似文献
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We present algorithmic lower bounds on the size sd of the largest independent sets of vertices in random d-regular graphs, for each fixed d≥3. For instance, for d=3 we prove that, for graphs on n vertices, sd≥0.43475n with probability approaching one as n tends to infinity. 相似文献
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A real x is called h-bounded computable , for some function h:N→N, if there is a computable sequence (xs) of rational numbers which converges to x such that, for any n∈N, at most h(n) non-overlapping pairs of its members are separated by a distance larger than 2-n. In this paper we discuss properties of h-bounded computable reals for various functions h. We will show a simple sufficient condition for a class of functions h such that the corresponding h-bounded computable reals form an algebraic field. A hierarchy theorem for h-bounded computable reals is also shown. Besides we compare semi-computability and weak computability with the h-bounded computability for special functions h. 相似文献
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Question/Answer games (Q/A games for short) are a generalization of the Rényi–Ulam game and they are a model for information extraction in parallel. A Q/A game, G=(D,s,(q1,…,qk)), is played on a directed acyclic graph, D=(V,E), with a distinguished start vertex s. In the ith round, Paul selects a set, Qi⊆V, of at most qi non-terminal vertices. Carole responds by choosing an outgoing edge from each vertex in Qi. At the end of k rounds, Paul wins if Carole’s answers define a unique path from the root to one of the terminal vertices in D. 相似文献
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We define a self-map Pal:F2→F2 of the free group on two generators a,b, using automorphisms of F2 that form a group isomorphic to the braid group B3. The map Pal restricts to de Luca’s right iterated palindromic closure on the submonoid generated by a,b. We show that Pal is continuous for the profinite topology on F2; it is the unique continuous extension of de Luca’s right iterated palindromic closure to F2. The values of Pal are palindromes and coincide with the elements g∈F2 such that abg and bag are conjugate. 相似文献
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Let G=(V,E) be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex v∈V has a demand d(v)∈Z+ and a cost c(v)∈R+, where Z+ and R+ denote the set of nonnegative integers and the set of nonnegative reals, respectively. The source location problem with vertex-connectivity requirements in a given graph G requires finding a set S of vertices minimizing ∑v∈Sc(v) such that there are at least d(v) pairwise vertex-disjoint paths from S to v for each vertex v∈V−S. It is known that if there exists a vertex v∈V with d(v)≥4, then the problem is NP-hard even in the case where every vertex has a uniform cost. In this paper, we show that the problem can be solved in O(|V|4log2|V|) time if d(v)≤3 holds for each vertex v∈V. 相似文献
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It has been shown that the underestimated by DFT/LDA(GGA) band-gap can be efficiently corrected by an averaging procedure of transition energies over a region close to the direct band-gap transition, which we call the Δ(EIG) method (the differences in the Kohn–Sham eigenvalues). For small excitations the averaging appears to be equivalent to the Δ(SCF) approach (differences in the self-consistent energies), which is a consequence of Janak’s theorem and has been confirmed numerically. The Gaussian distribution in k-space for electronic excitation has been used (occupation numbers in the Δ(SCF) or eigenenergy sampling in the Δ(EIG)). A systematic behavior of the k-space localization parameter σk correcting the band-gap has been observed in numerical experiments. On that basis some sampling schemes for band-gap correction have been proposed and tested in the prediction of the band-gap behavior in InxGa(1−x)N semiconducting alloy, and a very good agreement with independent calculations has been obtained. In the context of the work the issue of electron localization in the r-space has been discussed which, as it has been predicted by Mori-Sánchez et al. [P. Mori-Sánchez, A.J. Cohen, W. Yang, Phys. Rev. Lett. 100 (2008) 146401], should reduce the effect of the convex behavior of the LDA/GGA functionals and improve the band-gap prediction within DFT/LDA(GGA). A scheme for electron localization in r-space has been suggested. 相似文献
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We consider orthogonal drawings of a plane graph G with specified face areas. For a natural number k, a k-gonal drawing of G is an orthogonal drawing such that the boundary of G is drawn as a rectangle and each inner face is drawn as a polygon with at most k corners whose area is equal to the specified value. In this paper, we show that every slicing graph G with a slicing tree T and a set of specified face areas admits a 10-gonal drawing D such that the boundary of each slicing subgraph that appears in T is also drawn as a polygon with at most 10 corners. Such a drawing D can be found in linear time. 相似文献
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In the paper two problems of a single machine bicriterion scheduling of a set of deteriorating jobs are considered. The jobs are independent, nonpreemptable and are ready for processing at time 0. The processing time pj of each job is a linear function of the starting time Sj of the job, pj=1+αjSj, where Sj?0 and αj>0 for j=0,1,...,n. 相似文献
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Given a graph G, an integer k, and a demand set D={(s1,t1),…,(sl,tl)}, the k-Steiner Forest problem finds a forest in graph G to connect at least k demands in D such that the cost of the forest is minimized. This problem was proposed by Hajiaghayi and Jain in SODA’06. Thereafter, using a Lagrangian relaxation technique, Segev et al. gave the first approximation algorithm to this problem in ESA’06, with performance ratio O(n2/3logl). We give a simpler and faster approximation algorithm to this problem with performance ratio O(n2/3logk) via greedy approach, improving the previously best known ratio in the literature. 相似文献
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This paper aims at investigating properties of homomorphisms which preserve the bordered words. The bordered words are classified into d1-words and d2-words, where the length of the proper border of d2-word is greater than half of it. Some characterizations of d1-word-preserving homomorphism are studied. Some relationships among d-primitivity-preserving homomorphisms, d1-word-preserving homomorphisms, and d2-word-preserving homomorphisms are investigated. We show that every d-primitivity-preserving homomorphism is d1-word-preserving and every d1-word-preserving homomorphism is d2-word-preserving. 相似文献