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 show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n(omega) + n(2+o(1))), where omega is the exponent of the fastest matrix multi...
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We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n(omega) + n(2+o(1))), where omega is the exponent of the fastest matrix multiplication algorithm. By the currently best bound on omega, the running time of our algorithm is O(n(2.376)). Our algorithm substantially improves the previous time-bounds for this problem, and its asymptotic time complexity matches that of the fastest known algorithm for finding any triangle (not necessarily a maximum-weight one) in a graph. We can extend our algorithm to improve the upper bounds on finding a maximum-weight triangle in a sparse graph and on finding a maximum-weight subgraph isomorphic to a fixed graph. We can find a maximum-weight triangle in a vertex-weighted graph with m edges in asymptotic time required by the fastest algorithm for finding any triangle in a graph with m edges, i.e., in time O(m(1.41)). Our algorithms for a maximum-weight fixed subgraph (in particular any clique of constant size) are asymptotically as fast as the fastest known algorithms for a fixed subgraph.
A method to relabel noisy multi-criteria data sets is presented, taking advantage of the transitivity of the non-monotonicity relation to formulate the problem as an efficiently solvable maximum independent set proble...
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A method to relabel noisy multi-criteria data sets is presented, taking advantage of the transitivity of the non-monotonicity relation to formulate the problem as an efficiently solvable maximum independent set problem. A framework and an algorithm for general loss functions are presented. and the flexibility of the approach is indicated by some examples, showcasing the ease with which the method can handle application-specific loss functions. Both didactical examples and real-life applications are provided, using the zero-one, the L1 and the squared loss functions, as well as combinations thereof. (C) 2009 Elsevier Inc. All rights reserved.
Based on the mobile automaton model, an algorithm is introduced that grows planar, trivalent graphs by exhibiting a peculiar, twofold dynamics. In a first phase, graph growth appears to be pseudo-random and O(n) then ...
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Based on the mobile automaton model, an algorithm is introduced that grows planar, trivalent graphs by exhibiting a peculiar, twofold dynamics. In a first phase, graph growth appears to be pseudo-random and O(n) then it settles to a very regular behavior and O(root n) rate. A pseudo-random O(root n) mobile automaton is already known;the new automaton provides now a finite, but surprisingly long, pseudo-random, linear growth process. Applications of mobile automata to fundamental physics and quantum gravity have been recently suggested. (C) 2009 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 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 define and study a family of optimization problems called FERRY problems, which may be viewed as generalizations of the classical wolf-goat-cabbage puzzle. We present the FERRY COVER problem (FC), whe...
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In this paper we define and study a family of optimization problems called FERRY problems, which may be viewed as generalizations of the classical wolf-goat-cabbage puzzle. We present the FERRY COVER problem (FC), where the objective is to determine the minimum required boat size to safely transport n items represented by a graph G and demonstrate a close connection with VERTEX COVER which leads to hardness and approximation results. We also completely solve the problem on trees. Then we focus on a variation of the same problem with the added constraint that only 1 round-trip is allowed (FC1). We present a reduction from MAX-NAE{3}-SAT which shows that this problem is NP-hard and APX-hard. We also provide an approximation algorithm for bipartite graphs with a factor asymptotically equal to 4/3 and a 1.56-approximation algorithm for planar graphs. Finally, we generalize the above problem to define FCm, where at most m round-trips are allowed, and MFTk, which is the problem of minimizing the number of round-trips when the boat capacity is k. We present some preliminary lemmata for both, which provide bounds on the value of the optimal solution, and relate them to FC.
In this paper, the mutual exclusion scheduling problem is addressed. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times....
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In this paper, the mutual exclusion scheduling problem is addressed. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times. When restricted to interval graphs or related classes like circular-arc graphs and tolerance graphs, the problem has some applications in workforce planning. Unfortunately, the problem is shown to be NP-hard for interval graphs, even if k is a constant greater than or equal to four [H.L. Bodlaencler and K. Jansen Restrictions of graph partition problems. Part 1, Theoretical Computer Science 148(1995) pp. 93-109]. Several polynomial-time solvable cases significant in practice are exhibited here, for which we took care to devise simple and efficient algorithms (in particular linear-time and space algorithms). On the other hand, by reinforcing the NP-hardness result of Bodlaender and Jansen, we obtain a more precise cartography of the complexity of the problem for the classes of graphs studied. (c) 2008 Elsevier B.V. All rights reserved.
Let G=(V, E, w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G' be obtained from G by an application of a set of edge weight updates to G. Let s is an element of V and let T-s a...
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Let G=(V, E, w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G' be obtained from G by an application of a set of edge weight updates to G. Let s is an element of V and let T-s and T'(s) be Shortest Path Trees (SPTs) rooted at s in G and G', respectively. The Dynamic Shortest Path ( DSP) problem is to compute T'(s) from Ts. Existing work on this problem focuses on either a single edge weight change or multiple edge weight changes in which some of them are incorrect or are not optimized. We correct and extend a few state-of-the-art dynamic SPT algorithms to handle multiple edge weight updates. We prove that these algorithms are correct. Dynamic algorithms may not outperform static algorithms all the time. To evaluate the proposed dynamic algorithms, we compare them with the well-known static Dijkstra algorithm. Extensive experiments are conducted with both real-life and artificial data sets. The experimental results suggest the most appropriate algorithms to be used under different circumstances.
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.
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