Results 1  10
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15
Multimedia Communication
 Proceedings of the IEEE
, 1997
"... : Multimedia communication deals with the transfer, the protocols, services and mechanisms of discrete media data (such as text and graphics) and continuous media data (like audio and video) in/over digital networks. Such a communication requires all involved components to be capable of handling a w ..."
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Cited by 41 (0 self)
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: Multimedia communication deals with the transfer, the protocols, services and mechanisms of discrete media data (such as text and graphics) and continuous media data (like audio and video) in/over digital networks. Such a communication requires all involved components to be capable of handling a welldefined quality of service. The most important quality of service parameters are used to request (1) the required capacities of the involved resources, (2) compliance to endtoend delay and jitter as timing restrictions, and (3) restriction of the loss characteristics. In this paper we describe the necessary issues and we study the ability of current networks and communication systems to support distributed multimedia applications. Further, we discuss upcoming approaches and systems which promise to provide the necessary mechanisms and consider which issues are missing for a complete multimedia communication infrastructure. Keywords: multimedia, communication, quality of service, reser...
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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Cited by 17 (7 self)
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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.
Shortest paths in planar graphs with real lengths in O(n log 2 n/ log log n) time
 Proc. 18th
, 2010
"... Abstract. Givenannvertexplanardirectedgraphwithrealedgelengths andwithnonegativecycles,weshowhowtocomputesinglesourceshortest path distances in the graph in O(nlog 2 n/loglogn) time with O(n) space. This improves on a recent O(nlog 2 n) time bound by Klein et al. 1 ..."
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Cited by 11 (4 self)
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Abstract. Givenannvertexplanardirectedgraphwithrealedgelengths andwithnonegativecycles,weshowhowtocomputesinglesourceshortest path distances in the graph in O(nlog 2 n/loglogn) time with O(n) space. This improves on a recent O(nlog 2 n) time bound by Klein et al. 1
Minimum Cuts and Shortest NonSeparating Cycles via Homology Covers
 SYMPOSIUM ON DISCRETE ALGORITHMS
, 2011
"... Let G be a directed graph with weighted edges, embedded on a surface of genus g with b boundaries. We describe an algorithm to compute the shortest directed cycle in G in any given � 2homology class in 2 O(g+b) n log n time; this problem is NPhard even for undirected graphs. We also present two ap ..."
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Cited by 9 (3 self)
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Let G be a directed graph with weighted edges, embedded on a surface of genus g with b boundaries. We describe an algorithm to compute the shortest directed cycle in G in any given � 2homology class in 2 O(g+b) n log n time; this problem is NPhard even for undirected graphs. We also present two applications of our algorithm. The first is an algorithm to compute the shortest nonseparating directed cycle in G in 2 O(g) n log n time, improving the recent algorithm of Cabello et al. [SOCG 2010] for all g = o(log n). The second is a combinatorial algorithm to compute minimum (s, t)cuts in undirected surface graphs in 2 O(g) n log n time, improving an algorithm of Chambers et al. [SOCG 2009] for all positive g. Unlike earlier algorithms for surface graphs that construct and search finite portions of the universal cover, our algorithms use another canonical covering space, called the Z 2homology cover.
Finding shortest nontrivial cycles in directed graphs on surfaces
 In These Proceedings
, 2010
"... Let D be a weighted directed graph cellularly embedded in a surface of genus g, orientable or not, possibly with boundary. We describe algorithms to compute a shortest noncontractible and a shortest surface nonseparating cycle in D. This generalizes previous results that only dealt with undirected ..."
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Cited by 9 (3 self)
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Let D be a weighted directed graph cellularly embedded in a surface of genus g, orientable or not, possibly with boundary. We describe algorithms to compute a shortest noncontractible and a shortest surface nonseparating cycle in D. This generalizes previous results that only dealt with undirected graphs. Our first algorithm computes such cycles in O(n 2 log n) time, where n is the total number of vertices and edges of D, thus matching the complexity of the best known algorithm in the undirected case. It revisits and extends Thomassen’s 3path condition; the technique applies to other families of cycles as well. We also give an algorithm with subquadratic complexity in the complexity of the input graph, if g is fixed. Specifically, we can solve the problem in O ( √ g n 3/2 log n) time, using a divideandconquer technique that simplifies the graph while preserving the topological properties of its cycles. A variant runs in O(ng log g + nlog 2 n) for graphs of bounded treewidth.
Hardness results for homology localization
 In SODA ’10: Proc. 21st Ann. ACMSIAM Sympos. Discrete Algorithms (2010
"... We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1norm of a cycle. Two main results are presented. First, we prove the problem is NPhard to approximate w ..."
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Cited by 8 (1 self)
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We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1norm of a cycle. Two main results are presented. First, we prove the problem is NPhard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NPhard to approximate even when the Betti number is O(1). A side effect is the inapproximability of the problem of computing the nonbounding cycle with the smallest volume, and computing cycles representing a homology basis with the minimal total volume. We also discuss other geometric measures (diameter and radius) and show their disadvantages in homology localization. Our work is restricted to homology over the Z2 field. 1
Maximum Flows and Parametric Shortest Paths in Planar Graphs
"... We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously ..."
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Cited by 6 (1 self)
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We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously increase the parameter, each change in the shortest path tree can be effected in O(log n) time using standard dynamic tree data structures, and the special structure of the parametrization implies that each directed edge enters the evolving shortest path tree at most once. The resulting maximumflow algorithm is identical to the recent algorithm of Borradaile and Klein [J. ACM 2009], but our new formulation allows a simpler presentation and analysis. On the other hand, we demonstrate that for a similarly structured parametric shortest path problem on the torus, the shortest path tree can change Ω(n²) times in the worst case, suggesting that a different method may be required to efficiently compute maximum flows in highergenus graphs.
Shortest nontrivial cycles in directed surface graphs
 In Proc. 27th Ann. Symp. Comput. Geom
, 2011
"... Let G be a directed graph embedded on a surface of genus g. We describe an algorithm to compute the shortest nonseparating cycle in G in O(g 2 n log n) time, exactly matching the fastest algorithm known for undirected graphs. We also describe an algorithm to compute the shortest noncontractible cy ..."
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Cited by 4 (2 self)
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Let G be a directed graph embedded on a surface of genus g. We describe an algorithm to compute the shortest nonseparating cycle in G in O(g 2 n log n) time, exactly matching the fastest algorithm known for undirected graphs. We also describe an algorithm to compute the shortest noncontractible cycle in G in g O(g) n log n time, matching the fastest algorithm for undirected graphs of constant genus.
Global Minimum Cuts in Surface Embedded Graphs
"... We give a deterministic algorithm to find the minimum cut in a surfaceembedded graph in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in g O(g) n log log n time, matching the running time of the fastest algorithm kno ..."
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Cited by 2 (2 self)
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We give a deterministic algorithm to find the minimum cut in a surfaceembedded graph in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in g O(g) n log log n time, matching the running time of the fastest algorithm known for planar graphs, due to Ł ˛acki and Sankowski, for any constant g. Indeed, our algorithm calls Ł ˛acki and Sankowski’s recent O(n log log n) time planar algorithm as a subroutine. Previously, the best time bounds known for this problem followed from two algorithms for general sparse graphs: a randomized algorithm of Karger that runs in O(n log 3 n) time and succeeds with high probability, and a deterministic algorithm of Nagamochi and Ibaraki that runs in O(n 2 log n) time. We can also achieve a deterministic g O(g) n 2 log log n time bound by repeatedly applying the best known algorithm for minimum (s, t)cuts in surface graphs. The bulk of our work focuses on the case where the dual of the minimum cut splits the underlying surface into multiple components with positive genus. 1
Branching and Circular Features in High Dimensional Data
, 2011
"... Large observations and simulations in scientific research give rise to highdimensional data sets that present many challenges and opportunities in data analysis and visualization. Researchers in the application domains such as engineering, computational biology, climate study, imaging and motion ca ..."
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Cited by 2 (1 self)
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Large observations and simulations in scientific research give rise to highdimensional data sets that present many challenges and opportunities in data analysis and visualization. Researchers in the application domains such as engineering, computational biology, climate study, imaging and motion capture are faced with the problem of how to discover compact representations of highdimensional data while preserving their intrinsic structure. In many applications, the original data is projected onto lowdimensional space via dimensionality reduction techniques prior to modeling. One problem with this approach is that the projection step in the process can fail to preserve structure in the data that is only apparent in high dimensions. Conversely, such techniques may create structural illusions in the projection, implying structure not present in the original highdimensional data. Our solution is to utilize topological techniques to recover important structures in highdimensional data that contains nontrivial topology. Specifically, we are interested in two types of features in high dimensions: local branching structures and global circular structures. We construct local and global circlevalued coordinate functions to represent such features. Subsequently, we perform dimensionality reduction on the data while ensuring such structures are visually preserved. Our results reveal neverbeforeseen structures on realworld data sets from a variety of applications. Branching and Circular Features in High Dimensional Data