This paper proposes a deterministic importance sampling algorithm that is based on the recognition that delta-sigma modulation is equivalent to importance sampling. We propose a generalization for delta-sigma modulati...
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This paper proposes a deterministic importance sampling algorithm that is based on the recognition that delta-sigma modulation is equivalent to importance sampling. We propose a generalization for delta-sigma modulation in arbitrary dimensions, taking care of the curse of dimensionality as well. Unlike previous sampling techniques that transform low-discrepancy and highly stratified samples in the unit cube to the integration domain, our error diffusion sampler ensures the proper distribution and stratification directly in the integration domain. We also present applications, including environment mapping and global illumination rendering with virtual point sources.
We present algorithms for computing small stretch (alpha, beta)-spanners in the streaming model. An (alpha, beta)-spanner of a graph G is a subgraph S subset of G such that for each pair of vertices the distance in S ...
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We present algorithms for computing small stretch (alpha, beta)-spanners in the streaming model. An (alpha, beta)-spanner of a graph G is a subgraph S subset of G such that for each pair of vertices the distance in S is at most alpha times the distance in G plus beta. We assume that the graph is given as a stream of edges and vertices, and that only one pass over the data is allowed. Furthermore, the number of vertices and edges are not known in advance. We denote by m the current number of scanned edges and by n the current number of discovered vertices. In this model we show how to compute a (k, k - 1)-spanner of an unweighted undirected graph, for k = 2, 3, in O(1) amortized processing time per edge/vertex. The computed (k, k - 1)-spanners have O(n(1+1/k)) edges and our algorithms use only O(n(1+1/k)) words of memory space. In case only H(n) internal memory is available, the same spanners can be computed using O(n(1+1/k)/B) external memory blocks, each of size B. Each edge/vertex is processed in O(1) amortized time, plus O(1/B) amortized block transfers. (C) 2008 Elsevier B.V. All rights reserved.
In the present paper, a procedure is developed for fully automatic recognition of the frontal sinus in cranial radiographs. An X-ray image of a whole skull is required at the input of the procedure, which consists of ...
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In the present paper, a procedure is developed for fully automatic recognition of the frontal sinus in cranial radiographs. An X-ray image of a whole skull is required at the input of the procedure, which consists of three subsequent steps: the selection of a rectangular region of interest, containing the sinus;detection of the line of brow ridges;and fronto-nasal suture, detection of the borders of the frontal sinus. The recognition algorithm is based on a method of connectivity-preserving thresholding, introduced in the present study, and on watersheds from markers. Totally, 50 X-ray images have been analyzed. The frontal sinus borders were recognized correctly in 41 cases.
We study the problem of adding an inclusion minimal set of edges to a given arbitrary graph so that the resulting graph is a split graph, called a minimal split completion of the input graph. Minimal completions of ar...
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We study the problem of adding an inclusion minimal set of edges to a given arbitrary graph so that the resulting graph is a split graph, called a minimal split completion of the input graph. Minimal completions of arbitrary graphs into chordal and interval graphs have been studied previously, and new results have been added recently. We extend these previous results to split graphs by giving a linear-time algorithm for computing minimal split completions. We also give two characterizations of minimal split completions, which lead to a linear time algorithm for extracting a minimal split completion from any given split completion. We prove new properties of split graph that are both useful for our algorithms and interesting on their own. First, we present a new way of partitioning the vertices of a split graph uniquely into three subsets. Second, we prove that split graphs have the following property: given two split graphs on the same vertex set where one is a subgraph of the other, there is a sequence of edges that can be removed from the larger to obtain the smaller such that after each edge removal the modified graph is split. (C) 2008 Elsevier B.V. All rights reserved,
In this paper, we introduce a combinatorial algorithm for the message scheduling problem on Time Division Multiple Access ( TDMA) networks. In TDMA networks, time is divided in to slots in which messages are scheduled...
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In this paper, we introduce a combinatorial algorithm for the message scheduling problem on Time Division Multiple Access ( TDMA) networks. In TDMA networks, time is divided in to slots in which messages are scheduled. The frame length is defined as the total number of slots required for all stations to broadcast without message collisions. The objective is to provide a broadcast schedule of minimum frame length which also provides the maximum throughput. This problem is known to be NP-hard, thus efficient heuristics are needed to provide solutions to real-world instances. We present a two-phase algorithm which exploits the combinatorial structure of the problem in order to provide high quality solutions. The first phase finds a feasible frame length in which the throughput is maximized in phase two. Computational results are provided and compared with other heuristics in the literature as well as to the optimal solutions found using a commercial integer programming solver. Experiments on 63 benchmark instances show that the proposed method is able to provide optimal frame lengths for all cases with near optimal throughput.
We present an algorithm that takes O(sort(N)) I/Os (sort(N) = Theta ((N/(DB)) log(M/B)(N/B)) is the number of I/Os it takes to sort N data items) to compute a tree decomposition of width at most k, for any graph G of ...
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We present an algorithm that takes O(sort(N)) I/Os (sort(N) = Theta ((N/(DB)) log(M/B)(N/B)) is the number of I/Os it takes to sort N data items) to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N, where k is a constant. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including the single-source shortest path problem and a number of problems that are NP-hard on general graphs. The tree decomposition can also be used to obtain an optimal separator decomposition of G. We use such a decomposition to perform depth-first search in G in O(N/(DB)) I/Os. As important tools that are used in the tree decomposition algorithm, we introduce flippable DAGs and present an algorithm that computes a perfect elimination ordering of a k-tree in O(sort(N)) I/Os. The second contribution of our paper, which is of independent interest, is a general and simple framework for obtaining I/O-efficient algorithms for a number of graph problems that can be solved using greedy algorithms in internal memory. We apply this framework in order to obtain an improved algorithm for finding a maximal matching and the first deterministic I/O-efficient algorithm for finding a maximal independent set of an arbitrary graph. Both algorithms take O(sort(|V| + |E|)) I/Os. The maximal matching algorithm is used in the tree decomposition algorithm.
A spanning tree T of a graph G is called a tree t-spanner, if the distance between any two vertices in T is at most t-times their distance in G. A graph that has a tree t-spanner is called a tree t-spanner admissible ...
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A spanning tree T of a graph G is called a tree t-spanner, if the distance between any two vertices in T is at most t-times their distance in G. A graph that has a tree t-spanner is called a tree t-spanner admissible graph. The problem of deciding whether a graph is tree t-spanner admissible is NP-complete for any fixed t >= 4, and is linearly solvable for t = 1 and t = 2. The case t = 3 still remains open. A directed path graph is called a 2-sep directed path graph if all of its minimal a - b vertex separator for every pair of non-adjacent vertices a and b are of size two. Le and Le [H.-O. Le,V.B. Le,Optimal tree 3-spanners in directed path graphs, Networks 34 (2) (1999) 81-87] showed that directed path graphs admit tree 3-spanners. However, this result has been shown to be incorrect by Panda and Das [B.S. Panda, Anita Das, On tree 3-spanners in directed path graphs, Networks 50 (3) (2007) 203-210]. In fact, this paper observes that even the class of 2-sep directed path graphs, which is a proper subclass of directed path graphs, need not admit tree 3-spanners in general. It, then, presents a structural characterization of tree 3-spanner admissible 2-sep directed path graphs. Based on this characterization, a linear time recognition algorithm for tree 3-spanner admissible 2-sep, directed path graphs is presented. Finally, a linear time algorithm to construct a tree 3-spanner of a tree 3-spanner admissible 2-sep directed path graph is proposed. (C) 2008 Elsevier B.V. All rights reserved.
The spanning tree problem is to find a tree that connects all the vertices of G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. Klein and Stein demons...
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The spanning tree problem is to find a tree that connects all the vertices of G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. Klein and Stein demonstrated that a spanning tree can be found in O(log n) time with O(n + m) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. Circular permutation graphs properly contain the set of permutation graphs as a subclass and are first introduced by Rotem and Urrutia. They provided O(n(2.376)) time recognition algorithm. Circular permutation graphs and their models find several applications in VLSI layout. In this paper, we propose an optimal parallel algorithm for constructing a spanning tree on circular permutation graphs. It runs in O(log n) time with O(n/ log n) processors on the EREW PRAM.
Due to their ability to detect clusters with irregular boundaries, minimum spanning tree-based clustering algorithms have been widely used in practice. However, in such clustering algorithms, the search for nearest ne...
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Due to their ability to detect clusters with irregular boundaries, minimum spanning tree-based clustering algorithms have been widely used in practice. However, in such clustering algorithms, the search for nearest neighbor in the construction of minimum spanning trees is the main source of computation and the standard solutions take O(N(2)) time. In this paper, we present a fast minimum spanning tree-inspired clustering algorithm, which, by using an efficient implementation of the cut and the cycle property of the minimum spanning trees, can have much better performance than O(N(2))
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