共查询到20条相似文献,搜索用时 406 毫秒
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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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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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The most natural and perhaps most frequently used method for testing membership of an individual tuple in a conjunctive query is based on searching trees of partial solutions, or search-trees. We investigate the question of evaluating conjunctive queries with a time-bound guarantee that is measured as a function of the size of the optimal search-tree. We provide an algorithm that, given a database D, a conjunctive query Q, and a tuple a, tests whether Q(a) holds in D in time bounded by a polynomial in (sn)logk(sn)loglogn and nr, where n is the size of the domain of the database, k is the number of bound variables of the conjunctive query, s is the size of the optimal search-tree, and r is the maximum arity of the relations. In many cases of interest, this bound is significantly smaller than the nO(k) bound provided by the naive search-tree method. Moreover, our algorithm has the advantage of guaranteeing the bound for any given conjunctive query. In particular, it guarantees the bound for queries that admit an equivalent form that is much easier to evaluate, even when finding such a form is an NP-hard task. Concrete examples include the conjunctive queries that can be non-trivially folded into a conjunctive query of bounded size or bounded treewidth. All our results translate to the context of constraint-satisfaction problems via the well-publicized correspondence between both frameworks. 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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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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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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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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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 show how to compute Hong’s bound for the absolute positiveness of a polynomial in d variables with maximum degree δ in O(nlogdn) time, where n is the number of non-zero coefficients. For the univariate case, we give a linear time algorithm. As a consequence, the time bounds for the continued fraction algorithm for real root isolation improve by a factor of δ. 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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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 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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This work is concerned with simulating nondeterministic one-reversal multicounter automata (NCMs) by nondeterministic partially blind multihead finite automata (NFAs). We show that any one-reversal NCM with k counters can be simulated by a partially blind NFA with k blind heads. This provides a nearly complete categorization of the computational power of partially blind automata, showing that the power of a (k+1)-NFA lies between that of a k-NCM and a (k+1)-NCM. 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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Efficient characteristic set methods for computing zeros of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of zeros of a proper and monic triangular set is given. An improved zero decomposition algorithm is proposed to reduce the zero set of an equation system to the union of zero sets of monic proper triangular sets. The bitsize complexity of this algorithm is shown to be O(ln) for Boolean polynomials, where n is the number of variables and l≥2 is the number of equations. We also give a multiplication free characteristic set method for Boolean polynomials, where the sizes of the polynomials occurred during the computation do not exceed the sizes of the input polynomials and the bitsize complexity of algorithm is O(nd) for input polynomials with n variables and degree d. The algorithms are implemented in the case of Boolean polynomials and extensive experiments show that they are quite efficient for solving certain classes of Boolean equations raising from stream ciphers. 相似文献