Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z(n) only certain special (e.g. periodic or octagonal) sequences were investigated. In this p...
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Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z(n) only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretical criteria for certain important (e.g. metrical) properties of the sequences. Our results are valid for several types of classical neighborhood sequences and for generated distance functions (e.g. octagonal and chamfer distances) which are widely applied in digital image processing. We conclude the paper by showing how our results contribute to the theory of distance transformations. (D 2007 Elsevier B.V. All rights reserved.
A distance sensitivity oracle is a data structure answering queries that ask the shortest distance from a node to another in a network expecting node/edge failures. It has been mainly studied in theory literature, but...
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A distance sensitivity oracle is a data structure answering queries that ask the shortest distance from a node to another in a network expecting node/edge failures. It has been mainly studied in theory literature, but all the existing oracles for a directed graph suffer from prohibitive preprocessing time and space. Motivated by this, we develop two practical distance sensitivity oracles for directed graphs as variants of Transit Node Routing. The first oracle consists of a novel fault-tolerant index structure, which is used to construct a solution path and to detect and localize the impact of network failures, and an efficient query algorithm for it. The second oracle is made by applying the A* heuristics to the first oracle, which exploits lower bound distances to effectively reduce search space. In addition, we propose additional speed-up techniques to make our oracles faster with a slight loss of accuracy. We conduct extensive experiments with real-life datasets, which demonstrate that our oracles greatly outperform all of competitors in most cases. To the best of our knowledge, our oracles are the first distance sensitivity oracles that handle real-world graph data with million-level nodes.
A distance sensitivity oracle is a data structure answering queries that ask the shortest distance from a node to another in a network expecting node/edge failures. It has been mainly studied in theory literature, but...
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ISBN:
(数字)9781728129037
ISBN:
(纸本)9781728129037
A distance sensitivity oracle is a data structure answering queries that ask the shortest distance from a node to another in a network expecting node/edge failures. It has been mainly studied in theory literature, but all the existing oracles for a directed graph suffer from prohibitive preprocessing time and space. Motivated by this, we develop two practical distance sensitivity oracles for directed graphs as variants of Transit Node Routing, and effective speed-up techniques with a slight loss of accuracy. Extensive experiments demonstrate that our oracles greatly outperform all of competitors in most cases. To the best of our knowledge, our oracles are the first distance sensitivity oracles that handle real-world graph data with million-level nodes.
We present a randomized algorithm that computes single-source shortest paths (SSSP) in O(mlog(8)(n) logW) time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight ...
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ISBN:
(纸本)9781665455190
We present a randomized algorithm that computes single-source shortest paths (SSSP) in O(mlog(8)(n) logW) time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are (O) over tilde ((m + n(1.5)) logW) [BLNPSSSW FOCS'20] and m(4/3+o(1)) logW [AMV FOCS'20]. Near-linear time algorithms were known previously only for the special case of planar directed graphs [Fakcharoenphol and Rao FOCS'01]. In contrast to all recent developments that rely on sophisticated continuous optimization methods and dynamic algorithms, our algorithm is simple: it requires only a simple graph decomposition and elementary combinatorial tools. In fact, ours is the first combinatorial algorithm for negative-weight SSSP to break through the classic (O) over tilde (m root n logW) bound from over three decades ago [Gabow and Tarjan SICOMP'89].
The girth of a graph G is the length of a shortest cycle of G. In this article we design an O(n(5/4) log n) algorithm for finding the girth of an undirected n-vertex planar graph, the first o(n(2)) algorithm for this ...
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The girth of a graph G is the length of a shortest cycle of G. In this article we design an O(n(5/4) log n) algorithm for finding the girth of an undirected n-vertex planar graph, the first o(n(2)) algorithm for this problem. We also extend our results for the class of graphs embedded into an orientable surface of small genus. Our approach uses several techniques such as graph partitioning, hammock decomposition, graph covering, and dynamic shortest-path computation. We discuss extensions and generalizations of our result.
A genetic map is an ordering of genetic markers calculated from a population of known lineage. Although, traditionally, a map has been generated from a single population for each species, recently, researchers have cr...
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A genetic map is an ordering of genetic markers calculated from a population of known lineage. Although, traditionally, a map has been generated from a single population for each species, recently, researchers have created maps from multiple populations. In the face of these new data, we address the need to find a consensus map - a map that combines the information from multiple partial and possibly inconsistent input maps. We model each input map as a partial order and formulate the consensus problem as finding a median partial order. Finding the median of multiple total orders ( preferences or rankings) is a well-studied problem in social choice. We choose to find the median by using the weighted symmetric difference distance, which is a more general version of both the symmetric difference distance and the Kemeny distance. Finding a median order using this distance is NP-hard. We show that, for our chosen weight assignment, a median order satisfies the positive responsiveness, extended Condorcet, and unanimity criteria. Our solution involves finding the maximum acyclic subgraph of a weighted directed graph. We present a method that dynamically switches between an exact branch and bound algorithm and a heuristic algorithm and show that, for real data from closely related organisms, an exact median can often be found. We present experimental results by using seven populations of the crop plant Zea mays.
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