Results 1  10
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14
Minimum Cuts and Shortest Homologous Cycles
 SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2009
"... We describe the first algorithms to compute minimum cuts in surfaceembedded graphs in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s, t)cut in g O(g) n log n time. Except for the spec ..."
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We describe the first algorithms to compute minimum cuts in surfaceembedded graphs in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s, t)cut in g O(g) n log n time. Except for the special case of planar graphs, for which O(n log n)time algorithms have been known for more than 20 years, the best previous time bounds for finding minimum cuts in embedded graphs follow from algorithms for general sparse graphs. A slight generalization of our minimumcut algorithm computes a minimumcost subgraph in every Z2homology class. We also prove that finding a minimumcost subgraph homologous to a single input cycle is NPhard.
On feedback vertex set new measure and new structures
 of Lecture Notes in Computer Science
, 2010
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An Orientation Theorem with Parity Conditions
, 2000
"... Given a graph G = (V, E) and a set T ⊆ V, an orientation of G is called Todd if precisely the vertices of T get odd indegree. We give a good characterization for the existence of a Todd orientation for which there exist k edgedisjoint spanning arborescences rooted at a prespecified set of k root ..."
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Cited by 5 (0 self)
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Given a graph G = (V, E) and a set T ⊆ V, an orientation of G is called Todd if precisely the vertices of T get odd indegree. We give a good characterization for the existence of a Todd orientation for which there exist k edgedisjoint spanning arborescences rooted at a prespecified set of k roots. Our result implies NashWilliams’ theorem on covering the edges of a graph by k forests and a (generalization of a) theorem due to Nebesky on upper embeddable graphs.
Algebraic Algorithms for Linear Matroid Parity Problems
"... We present fast and simple algebraic algorithms for the linear matroid parity problem and its applications. For the linear matroid parity problem, we obtain a simple randomized algorithm with running time O(mrω−1) where m and r are the number of columns and the number of rows and ω ≈ 2.376 is the ma ..."
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Cited by 4 (1 self)
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We present fast and simple algebraic algorithms for the linear matroid parity problem and its applications. For the linear matroid parity problem, we obtain a simple randomized algorithm with running time O(mrω−1) where m and r are the number of columns and the number of rows and ω ≈ 2.376 is the matrix multiplication exponent. This improves the O(mrω)time algorithm by Gabow and Stallmann, and matches the running time of the algebraic algorithm for linear matroid intersection, answering a question of Harvey. We also present a very simple alternative algorithm with running time O(mr2) which does not need fast matrix multiplication. We further improve the algebraic algorithms for some specific graph problems of interest. For the Mader’s disjoint Spath problem, we present an O(nω)time randomized algorithm where n is the number of vertices. This improves the running time of the existing results considerably, and matches the running time of the algebraic algorithms for graph matching. For the graphic matroid parity problem, we give an O(n4)time randomized algorithm where n is the number of vertices, and an O(n3)time randomized algorithm for a special case useful in designing approximation algorithms. These algorithms are optimal in terms of n as the input size could be Ω(n4) and Ω(n3) respectively. The techniques are based on the algebraic algorithmic framework developed by Mucha and Sankowski, Harvey, and Sankowski. While linear matroid parity and Mader’s disjoint Spath are challenging generalizations for the design of combinatorial algorithms, our results show that both the algebraic algorithms for linear matroid intersection and graph matching can be extended nicely to more general settings. All algorithms are still faster than the existing algorithms even if fast matrix multiplication is not used. These provide simple algorithms that can be easily implemented in practice.
Extended Graph Rotation Systems as a Model for Cyclic Weaving on Orientable Surfaces
"... Abstract. Our interest in computer graphics motivates a revised study of graph rotation systems, which are constructs by which topological graph theorists specify the placement of graphs on surfaces, nonorientable as well as orientable. Whereas orientable imbeddings have been studied extensively, n ..."
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Abstract. Our interest in computer graphics motivates a revised study of graph rotation systems, which are constructs by which topological graph theorists specify the placement of graphs on surfaces, nonorientable as well as orientable. Whereas orientable imbeddings have been studied extensively, nonorientable imbeddings have been comparatively neglected. This study extends general rotation systems into a solid mathematical model for the development of an interactivegraphics cyclicweaving system. This involves a systematic exploration and characterization of dynamic surgery operations on graph rotation systems, such as edgeinsertion, edgedeletion, and edgetwisting, which are used within an interactivegraphics system for designing weavings. Some fundamental theoretical results for the model are derived. It will be seen how general rotation systems that induce nonorientable surfaces can specify weavings on orientable surfaces.
The genus distributions of 4regular digraphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 43 (2009), PAGES 79–90
, 2009
"... An embedding of an Eulerian digraph in orientable surfaces was introduced by Bonnington et al. They gave some problems which need to be further studied. One of them is whether the embedding distribution of an embeddable digraph is always unimodal. In this paper, we first introduce the method of how ..."
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Cited by 1 (0 self)
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An embedding of an Eulerian digraph in orientable surfaces was introduced by Bonnington et al. They gave some problems which need to be further studied. One of them is whether the embedding distribution of an embeddable digraph is always unimodal. In this paper, we first introduce the method of how to determine the faces and antifaces from a given rotation scheme of a digraph. The genus distributions of two new kinds of 4regular digraphs in orientable surfaces are obtained. The genus distributions of one kind of digraph are strong unimodal, which gives a partial answer to the above problem.
I Artificial Intelligence
, 1996
"... ther sensing devices in a general way. A modular system that allows new sensing devices to be added incrementally would be extremely useful. 2. Multiple sensing is in many ways a problem in distributed computation. Each sensor is typically a separate computing element, with its own world model and ..."
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ther sensing devices in a general way. A modular system that allows new sensing devices to be added incrementally would be extremely useful. 2. Multiple sensing is in many ways a problem in distributed computation. Each sensor is typically a separate computing element, with its own world model and set of primitives. Each sensor has its own resolution, bandwidth and response time and a major task in robotics is getting them all to work together. An open problem is the organization of such systems; should they be hierarchical with a top level controlling "overseer" or should they be more anarchistic, with each sensor doing its own thing and a minimum level of coordination. The answer is partially task dependent, but as sensors proliferate, the solutions become more difficult. 3. Tactile sensing is becoming more important in robotics. Machine vision researchers have benefited from trying to understand biological vision systems. Robotics can also benefit from an understanding of human ha
Yechiam Yemini
"... this paper are a bit outofdate: not quite as good as our new results reported above!) ..."
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this paper are a bit outofdate: not quite as good as our new results reported above!)
The Maximum Partition Matching Problem with Applications
"... Let S = fC 1 ; C 2 ; : : : ; C k g be a collection of pairwise disjoint subsets of U = f1; 2; : : : ; ng such that i=1 C i = U . A partition matching of S consists of two subsets fa 1 ; a 2 ; : : : ; am g and fb 1 ; b 2 ; : : : ; b m g of U together with a sequence of distinct partitions of S: (A ..."
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Let S = fC 1 ; C 2 ; : : : ; C k g be a collection of pairwise disjoint subsets of U = f1; 2; : : : ; ng such that i=1 C i = U . A partition matching of S consists of two subsets fa 1 ; a 2 ; : : : ; am g and fb 1 ; b 2 ; : : : ; b m g of U together with a sequence of distinct partitions of S: (A 1 ; B 1 ), (A 2 ; B 2 ), : : :, (Am ; Bm ) such that a i is contained in a subset in the collection A i and b i is contained in a subset in the collection B i for all i = 1; : : : ; m. An efficient algorithm is developed that constructs a maximum partition matching for a given collection S. The algorithm can be used to construct optimal parallel routing between two nodes in interconnection networks.