共查询到20条相似文献,搜索用时 312 毫秒
1.
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 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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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 study the state complexity of certain simple languages. If A is an alphabet of k letters, then a k-language is a nonempty set of words of length k, that is, a uniform language of length k. We show that the minimal state complexity of a k-language is k+2, and the maximal, (kk−1−1)/(k−1)+2k+1. We prove constructively that, for every i between the minimal and maximal bounds, there is a language of state complexity i. We introduce a class of automata accepting sets of words that are permutations of A; these languages define a complete hierarchy of complexities between k2−k+3 and 2k+1. The languages of another class of automata, based on k-ary trees, define a complete hierarchy of complexities between 2k+1 and (kk−1−1)/(k−1)+2k+1. This provides new examples of uniform languages of maximal complexity. 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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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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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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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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Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial nO(k) time brute force algorithm for finding a k-element solution, we try to give algorithms with uniformly polynomial (i.e., f(k)⋅nO(1)) running time. The main result is that if the ground set of a represented linear matroid is partitioned into blocks of size ?, then we can determine in randomized time f(k,?)⋅nO(1) whether there is an independent set that is the union of k blocks. As a consequence, algorithms with similar running time are obtained for other problems such as finding a k-element set in the intersection of ? matroids, or finding k terminals in a network such that each of them can be connected simultaneously to the source by ? disjoint paths. 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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A folded hypercube is basically a hypercube with additional links augmented, where the additional links connect all pairs of nodes with longest distance in the hypercube. In an n-dimensional folded hypercube, it has been shown that n+1 node-disjoint paths from one source node to other n+1 (mutually) distinct destination nodes, respectively, can be constructed in O(n4) time so that their maximal length is not greater than ⌈n/2⌉+1, where n+1 is the connectivity and ⌈n/2⌉ is the diameter. Besides, their maximal length is minimized in the worst case. In this paper, we further show that by minimizing the computations of minimal routing functions, these node-disjoint paths can be constructed in O(n3) time, which is more efficient, and is hard to be reduced because it must take O(n3) time to compute a minimal routing function by solving a corresponding maximum weighted bipartite matching problem with the best known algorithm. 相似文献
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We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using O(lgn) memory for a list of size n, the i’th back-step from the farthest point reached so far takes O(lgi) time in the worst case, while the overhead per forward step is at most ? for arbitrary small constant ?>0. An arbitrary sequence of forward and back steps is allowed. A full trade-off between memory usage and time per back-step is presented: k vs. kn1/k and vice versa. Our algorithms are based on a novel pebbling technique which moves pebbles on a virtual binary, or n1/k-ary, tree that can only be traversed in a pre-order fashion. 相似文献
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Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in D an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time solvable for acyclic digraphs. In general, MinLOB is NP-hard and we consider three parameterizations of MinLOB. We prove that two of them are NP-complete for every value of the parameter, but the third one is fixed-parameter tractable (FPT). The FPT parameterization is as follows: given a digraph D of order n and a positive integral parameter k, check whether D contains an out-branching with at most n−k leaves (and find such an out-branching if it exists). We find a problem kernel of order O(k2) and construct an algorithm of running time O(2O(klogk)+n6), which is an ‘additive’ FPT algorithm. We also consider transformations from two related problems, the minimum path covering and the maximum internal out-tree problems into MinLOB, which imply that some parameterizations of the two problems are FPT as well. 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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The most effective way to maximize the lifetime of a wireless sensor network (WSN) is to allocate initial energy to sensors such that they exhaust their energy at the same time. The lifetime of a WSN as well as an optimal initial energy allocation are determined by a network design. The main contribution of the paper is to show that the lifetime of a WSN can be maximized by an optimal network design. We represent the network lifetime as a function of the number m of annuli and show that m has significant impact on network lifetime. We prove that if the energy consumed by data transmission is proportional to dα+c, where d is the distance of data transmission and α and c are some constants, then for a circular area of interest with radius R, the optimal number of annuli that maximizes the network lifetime is m=R((α−1)/c)1/α for an arbitrary sensor density function. 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