共查询到20条相似文献,搜索用时 15 毫秒
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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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Let F(x,y) be a polynomial over a field K and m a nonnegative integer. We call a polynomial g over K an m-near solution of F(x,y) if there exists a c∈K such that F(x,g)=cxm, and the number c is called an m-value of F(x,y) corresponding to g. In particular, c can be 0. Hence, by viewing F(x,y)=0 as a polynomial equation over K[x] with variable y, every solution of the equation F(x,y)=0 in K[x] is also an m-near solution. We provide an algorithm that gives all m-near solutions of a given polynomial F(x,y) over K, and this algorithm is polynomial time reducible to solving one variable equations over K. We introduce approximate solutions to analyze the algorithm. We also give some interesting properties of approximate solutions. 相似文献
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The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. Given two functions, f and g, with domain sizes N and M(N≤M), respectively, and the same range, the goal of the problem is to find x and y such that f(x)=g(y). This problem has been considered in both quantum and classical settings in terms of query complexity. This paper describes an optimal algorithm that uses quantum walk to solve this problem. Our algorithm can be slightly modified to solve the more general problem of finding a tuple consisting of elements in the two function domains that has a prespecified property. It can also be generalized to find a claw of k functions for any constant integer k>1, where the domain sizes of the functions may be different. 相似文献
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Let f(X,Y)∈Z[X,Y] be an irreducible polynomial over Q. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of f, or more precisely, of f modulo some prime integer p. The same idea of choosing a p satisfying some prescribed properties together with LLL is used to provide a new strategy for absolute factorization of f(X,Y). We present our approach in the bivariate case but the techniques extend to the multivariate case. Maple computations show that it is efficient and promising as we are able to construct the algebraic extension containing one absolute factor of a polynomial of degree up to 400. 相似文献
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Andrej Muchnik Alexander Shen Mikhail Ustinov Nikolai Vereshchagin Michael Vyugin 《Theoretical computer science》2007
Assume that a program p on input a outputs b. We are looking for a shorter program q having the same property (q(a)=b). In addition, we want q to be simple conditional to p (this means that the conditional Kolmogorov complexity K(q|p) is negligible). In the present paper, we prove that sometimes there is no such program q, even in the case when the complexity of p is much bigger than K(b|a). We give three different constructions that use the game approach, probabilistic arguments and algebraic arguments, respectively. 相似文献
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A. Abouelaoualim K.Ch. Das L. Faria Y. Manoussakis C. Martinhon R. Saad 《Theoretical computer science》2008
This paper deals with the existence and search for properly edge-colored paths/trails between two, not necessarily distinct, vertices s and t in an edge-colored graph from an algorithmic perspective. First we show that several versions of the s−t path/trail problem have polynomial solutions including the shortest path/trail case. We give polynomial algorithms for finding a longest properly edge-colored path/trail between s and t for a particular class of graphs and characterize edge-colored graphs without properly edge-colored closed trails. Next, we prove that deciding whether there exist k pairwise vertex/edge disjoint properly edge-colored s−t paths/trails in a c-edge-colored graph Gc is NP-complete even for k=2 and c=Ω(n2), where n denotes the number of vertices in Gc. Moreover, we prove that these problems remain NP-complete for c-edge-colored graphs containing no properly edge-colored cycles and c=Ω(n). We obtain some approximation results for those maximization problems together with polynomial results for some particular classes of edge-colored graphs. 相似文献
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This paper concerns construction of additive stretched spanners with few edges for n-vertex graphs having a tree-decomposition into bags of diameter at most δ, i.e., the tree-length δ graphs. For such graphs we construct additive 2δ-spanners with O(δn+nlogn) edges, and additive 4δ-spanners with O(δn) edges. This provides new upper bounds for chordal graphs for which δ=1. We also show a lower bound, and prove that there are graphs of tree-length δ for which every multiplicative δ-spanner (and thus every additive (δ−1)-spanner) requires Ω(n1+1/Θ(δ)) edges. 相似文献
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We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system (O,?), where O is the set of abstract origamis and ? is a binary relation on O, that models fold . An abstract origami is a structure (Π,∽,?), where Π is a set of faces constituting an origami, and ∽ and ? are binary relations on Π, each representing adjacency and superposition relations between the faces. 相似文献
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Alix L.H. Chow Leana Golubchik Samir Khuller Yuan Yao 《Journal of Parallel and Distributed Computing》2012
We consider the following basic question: a source node wishes to stream an ordered sequence of packets to a collection of receivers, which are in K clusters. A node may send a packet to another node in its own cluster in one time step and to a node in a different cluster in Tc time steps (Tc>1). Each cluster has two special nodes. We assume that the source and the special nodes in each cluster have a higher capacity and thus can send multiple packets at each step, while all other nodes can both send and receive a packet at each step. We construct two (intra-cluster) data communication schemes, one based on multi-trees (using a collection of d-ary interior-disjoint trees) and the other based on hypercubes. The multi-tree scheme sustains streaming within a cluster with O(dlogN) maximum playback delay and O(dlogN) size buffers, while communicating with O(d) neighbors, where N is the maximum size of any cluster. We also show that this protocol is optimal when d=2 or 3. The hypercube scheme sustains streaming within a cluster, with O(log2(N)) maximum playback delay and O(1) size buffers, while communicating with O(log(N)) neighbors, for arbitrary N. In addition, we extend our multi-tree scheme to work when receivers depart and arrive over time. We also evaluate our dynamic schemes using simulations. 相似文献
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We prove that a polynomial f∈R[x,y] with t non-zero terms, restricted to a real line y=ax+b, either has at most 6t−4 zeros or vanishes over the whole line. As a consequence, we derive an alternative algorithm for deciding whether a linear polynomial y−ax−b∈K[x,y] divides a lacunary polynomial f∈K[x,y], where K is a real number field. The number of bit operations performed by the algorithm is polynomial in the number of non-zero terms of f, in the logarithm of the degree of f, in the degree of the extension K/Q and in the logarithmic height of a, b and f. 相似文献
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We consider a two-edge connected, undirected graph G=(V,E), with n nodes and m non-negatively real weighted edges, and a single source shortest paths tree (SPT) T of G rooted at an arbitrary node r. If an edge in T is temporarily removed, it makes sense to reconnect the nodes disconnected from the root by adding a single non-tree edge, called a swap edge , instead of rebuilding a new optimal SPT from scratch. In the past, several optimality criteria have been considered to select a best possible swap edge. In this paper we focus on the most prominent one, that is the minimization of the average distance between the root and the disconnected nodes. To this respect, we present an O(mlog2n) time and O(m) space algorithm to find a best swap edge for every edge of T, thus improving for m=o(n2/log2n) the previously known O(n2) time and space complexity algorithm. 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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