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Beyond Trees: MRF Inference via OuterPlanar Decomposition
, 2010
"... Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NPhard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate algorithms (e.g. Loopy Belief Propagation (BP) and Treereweighted (TRW) methods). This paper prese ..."
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Cited by 17 (1 self)
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outerplanar graphs, and propose an approximate inference algorithm called OuterPlanar Decomposition (OPD). OPD is a strict generalization of BP and TRW, and contains both of them as special cases. Our experiments show that this extension beyond trees is indeed very powerful – OPD outperforms current state
Beyond Trees: MAP Inference in MRFs via OuterPlanar Decomposition
"... Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NPhard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate algorithms (e.g. Loopy Belief Propagation (BP) and Treereweighted (TRW) methods). This paper pre ..."
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outerplanar graphs, and propose an approximate inference algorithm called OuterPlanar Decomposition (OPD). OPD is a strict generalization of BP and TRW, and contains both of them as special cases. Our experiments show that this extension beyond trees is indeed very powerful â OPD outperforms current
Fast algorithms for maintaining shortest paths in outerplanar and planar digraphs
 Proceedings, lOth International Symposium on Fundamentals of Computation Theory, LNCS 965
, 1995
"... Abstract. We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs with sublogarithmic query time. By choosing appropriate parameters we achieve continuous tradeoffs between the preprocessing, query, and update times. Our data structure is based on a recursi ..."
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Cited by 2 (0 self)
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recursive separator decomposition of the graph and it encodes the shortest paths between the members of a properly chosen subset of vertices. We apply this result to construct improved shortest path algorithms for dynamic planar digraphs. 1
PLANAR GRAPH DECOMPOSITION AND ALL PAIRS SHORTEST PATHS
, 1988
"... An algorithm is presented. for generating a succinct encoding of all pairs shortest path infonnation in a directed planar graph G with realvalued edge costs but no negative cycles. The algorithm runs in 0 (pn) time. where n is the number of vertices in G, andp is the minimum cardinality of a sub ..."
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Cited by 39 (0 self)
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subset of the faces that cover all vertices, taken over all planar embeddings of G. The algorithm is based on a decomposition of the graph into 0 (pn) outerplanar subgraphs satisfying certain separator properties. Lineartime algorithms are presented for various subproblems including that of finding
Approximate Tree Decompositions of Planar Graphs in Linear Time
"... Many algorithms have been developed for NPhard problems on graphs with small treewidth k. For example, all problems that are expressible in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth. It turns out that the bottleneck of many algorithms for NPha ..."
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Cited by 5 (0 self)
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exponential in k. Key words: tree decomposition, treewidth, branchwidth, rankwidth, planar graph, ℓouterplanar, linear
Decompositions of Objects Bounded by Algebraic Curves'
, 1987
"... We present a.n algorithm to decompose the edges of planar curved object so that the carrier polygon of decomposed boundary is a simple polygon. We also present an algoritbm to compute a simple characteristic carrier polygon. By refining this decomposition further and using the chords and wedges of d ..."
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Cited by 1 (0 self)
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of decomposed edges, we obtain an inner polygon (resp. an outer polygon) which is a simple polygon totally contained in (resp. totally containing) the object. We also consider various applications of these polygons to object decompositions and collisionavoidance planar robot motion planning problems.
A direct decomposition of 3connected planar graphs
 In Proceedings of the 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC05
, 2005
"... ABSTRACT. We present a decomposition strategy for cnets, i. e., rooted 3connected planar maps. The decomposition yields an algebraic equation for the number of cnets with a given number of vertices and a given size of the outer face. The decomposition also leads to a deterministic and polynomial ..."
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Cited by 6 (5 self)
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ABSTRACT. We present a decomposition strategy for cnets, i. e., rooted 3connected planar maps. The decomposition yields an algebraic equation for the number of cnets with a given number of vertices and a given size of the outer face. The decomposition also leads to a deterministic and polynomial
Numerical Simulation of Wave Propagation Phenomena in Vocal Tract and Domain Decomposition Method
, 29
"... INTRODUCTION We develop a finite element approximation method for the Helmholtz equation in some unbounded region\Omega 0 : \Gamma\Deltau \Gamma ! 2 u = 0 in\Omega 0 (1) and apply the method to the wave propagation phenomena in a vocal tract. For various time frequencies !, we solve the Helmho ..."
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's horn equation. In this research, we confine our study to the case in which the outer region consists of a semiinfinite cylinder, and we assume that the original three dimensional acoustic region is planar which enables us to reduce the problem into a two dimensinal
Using Cellular Graph Embeddings in Solving All Pairs Shortest Paths Problems
, 1990
"... An algorithm is presented for generating a succinct encoding of all pairs shortest path information in an nvertex directed graph G with O(n) edges. The edges have realvalued costs, but the graph contains no negative cycles. The algorithm runs in O('Y(G)n + ('Y(G))'log 'Y(G)) ..."
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Cited by 9 (0 self)
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;Y(G)) time, where 'Y(G) is a topological emhedding measure that we define. The algorithm uses a decomposition of the graph into O(y(G)) outerplanar subgraphs satisfying certain separator properties, and a lineartime algorithm is presented to find this decomposition.
Fixed parameter algorithms for planar dominating set and related problems
, 2000
"... We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c √ kn), where c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O ( � γ(G)), and that such a tree decomposition ca ..."
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Cited by 35 (10 self)
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We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c √ kn), where c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O ( � γ(G)), and that such a tree decomposition
Results 1  10
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