共查询到20条相似文献,搜索用时 968 毫秒
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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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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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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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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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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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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 investigate a periodic version of the Benjamin-Ono (BO) equation associated with a discrete Laplacian. We find some special solutions to this equation, and calculate the values of the first two integrals of motion I1 and I2 corresponding to these solutions. It is found that there exists a strong resemblance between them and the spectra for the Macdonald q-difference operators. To better understand the connection between these classical and quantum integrable systems, we consider the special degenerate case corresponding to q=0 in more detail. Namely, we give general solutions to this degenerate periodic BO, obtain explicit formulas representing all the integrals of motions In (n=1,2,…), and successfully identify it with the eigenvalues of Macdonald operators in the limit q→0, i.e. the limit where Macdonald polynomials tend to the Hall–Littlewood polynomials. 相似文献
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Let R[X]:=R[X1,…,Xn]. Pólya’s Theorem says that if a form (homogeneous polynomial) p∈R[X] is positive on the standard n-simplex Δn, then for sufficiently large N all the coefficients of (X1+?+Xn)Np are positive. The work in this paper is part of an ongoing project aiming to explain when Pólya’s Theorem holds for forms if the condition “positive on Δn” is relaxed to “nonnegative on Δn”, and to give bounds on N. Schweighofer gave a condition which implies the conclusion of Pólya’s Theorem for polynomials f∈R[X]. We give a quantitative version of this result and use it to settle the case where a form p∈R[X] is positive on Δn, apart from possibly having zeros at the corners of the simplex. 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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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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We investigate the group key management problem for broadcasting applications. Previous work showed that, in handling key updates, batch rekeying can be more cost effective than individual rekeying. One model for batch rekeying is to assume that every user has probability p of being replaced by a new user during a batch period with the total number of users unchanged. Under this model, it was recently shown that an optimal key tree can be constructed in linear time when p is a constant and in O(n4) time when p→0. In this paper, we investigate more efficient algorithms for the case p→0, i.e., when membership changes are sparse. We design an O(n) heuristic algorithm for the sparse case and show that it produces a nearly 2-approximation to the optimal key tree. Simulation results show that its performance is even better in practice. We also design a refined heuristic algorithm and show that it achieves an approximation ratio of 1+? for any fixed ?>0 and n, as p→0. Finally, we give another approximation algorithm for any p∈(0,0.693) which is shown to be quite good by our simulations. 相似文献
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We aim at finding the best possible seed values when computing a1/p using the Newton–Raphson iteration in a given interval. A natural choice of the seed value would be the one that best approximates the expected result. It turns out that in most cases, the best seed value can be quite far from this natural choice. When we evaluate a monotone function f(a) in the interval [amin,amax], by building the sequence xn defined by the Newton–Raphson iteration, the natural choice consists in choosing x0 equal to the arithmetic mean of the endpoint values. This minimizes the maximum possible distance between x0 and f(a). And yet, if we perform n iterations, what matters is to minimize the maximum possible distance between xn and f(a). In several examples, the value of the best starting point varies rather significantly with the number of iterations. 相似文献
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In this paper we discuss models and methods for solving the rooted distance constrained minimum spanning tree problem which is defined as follows: given a graph G=(V,E) with node set V={0,1,…,n} and edge set E, two integer weights, a cost ce and a delay we associated with each edge e of E, and a natural (time limit) number H, we wish to find a spanning tree T of the graph with minimum total cost and such that the unique path from a specified root node, node 0, to any other node has total delay not greater than H. This problem generalizes the well known hop-constrained spanning tree problem and arises in the design of centralized networks with quality of service constraints and also in package shipment with service guarantee constraints. We present three theoretically equivalent modeling approaches, a column generation scheme, a Lagrangian relaxation combined with subgradient optimization procedure, both based on a path formulation of the problem, and a shortest path (compact) reformulation of the problem which views the underlying subproblem as defined in a layered extended graph. We present results for complete graph instances with up to 40 nodes. Our results indicate that the layered graph path reformulation model is still quite good when the arc weights are reasonably small. Lagrangian relaxation combined with subgradient optimization procedure appears to work much better than column generation and seems to be a quite reasonable approach to the problem for large weight, and even small weight, instances. 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