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All Pairs Almost Shortest Paths
 SIAM Journal on Computing
, 1996
"... Let G = (V; E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive onesided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe g) time ..."
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Cited by 83 (8 self)
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Let G = (V; E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive onesided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe g) time algorithm APASP 2 for computing all distances in G with an additive onesided error of at most 2. The algorithm APASP 2 is simple, easy to implement, and faster than the fastest known matrix multiplication algorithm. Furthermore, for every even k ? 2, we describe an g) time algorithm APASP k for computing all distances in G with an additive onesided error of at most k.
Arc Minimization in Finite State Decoding Graphs with CrossWord Acoustic Context
 In Proc. ICSLP’02
, 2002
"... Recent approaches to large vocabulary decoding with finite state graphs have focused on the use of state minimization algorithms to produce relatively compact graphs. This paper extends the finite state approach by developing complementary arcminimization techniques. The use of these techniques in ..."
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Cited by 6 (2 self)
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Recent approaches to large vocabulary decoding with finite state graphs have focused on the use of state minimization algorithms to produce relatively compact graphs. This paper extends the finite state approach by developing complementary arcminimization techniques. The use of these techniques in concert with state minimization allows us to statically compile decoding graphs in which the acoustic models utilize a full word of crossword context. This is in significant contrast to typical systems which use only a single phone. We show that the particular arcminimization problem that arises is in fact an NPcomplete combinatorial optimization problem, and describe the reduction from 3SAT. We present experimental results that illustrate the moderate sizes and runtimes of graphs for the Switchboard task. 1.
A Simplification Algorithm for Visualizing the Structure of Complex Graphs
"... Complex graphs, ones containing thousands of nodes of high degree, are difficult to visualize. Displaying all of the nodes and edges of these graphs can create an incomprehensible cluttered output. This paper presents a simplification algorithm that may be applied to a complex graph in order to prod ..."
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Cited by 1 (0 self)
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Complex graphs, ones containing thousands of nodes of high degree, are difficult to visualize. Displaying all of the nodes and edges of these graphs can create an incomprehensible cluttered output. This paper presents a simplification algorithm that may be applied to a complex graph in order to produce a controlled thinning of the graph. Using importance metrics, the simplification process removes nodes from the graph, leaving the central structure for visualization and evaluation. The simplification algorithm consists of two steps, calculation of the importance metrics and pruning. Several metrics based on various topological graph properties are described. The metrics are then used in a pruning process to simplify the graph. Nodes, along with their corresponding edges, are removed from the graph, while maintaining the graph’s overall connectivity. This simplified graph provides a cleaner, more meaningful visual representation of the graph’s structure; thus aiding the analysis of the graph’s underlying data. 1
Finding one of many Disjoint Perfect Matchings in a Bipartite Graph
, 2002
"... We demonstrate how to find a perfect matching in a bipartite graph containing {\sqrt n \sigma^3} disjoint perfect matchings in time O(\sqrt n m/\sigma ). ..."
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We demonstrate how to find a perfect matching in a bipartite graph containing {\sqrt n \sigma^3} disjoint perfect matchings in time O(\sqrt n m/\sigma ).
BMC Systems Biology BioMed Central
, 2008
"... Research article On the origin of distribution patterns of motifs in biological networks ..."
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Research article On the origin of distribution patterns of motifs in biological networks
An introduction to Stream Data Management on Large Information Networks ∗
"... In recent times there has been a surge of large scale information networks arising in various application domains, ranging from communication networks, cellphone call networks, social networks, email networks, road traffic networks, financial transaction networks, to name a few. In such applications ..."
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In recent times there has been a surge of large scale information networks arising in various application domains, ranging from communication networks, cellphone call networks, social networks, email networks, road traffic networks, financial transaction networks, to name a few. In such applications there is a need to manage and process large data streams in nearreal time. Examples of such queries include finding breaking news in Twitter stream, detecting network intrusion from network communication data, detecting congestion from traffic information, and so on. Some of the key data management challenges in supporting such realtime stream processing are very high update rates, dynamic structural changes in the underlying networks, complex relationships between data items, low latency requirements for processing queries. In this paper we present an introduction to the problem of stream data management in large scale information networks. We present some of the related works in the area of stream data management, continuous aggregation queries in sensor networks, intrusion detection, and processing social network data streams. We also present a glimpse of our ongoing work to manage large graphs and efficiently evaluate realtime aggregation queries on them. 1
Imperfect Matchings in Bipartite Graphs
"... assignment problem; imperfect matching; minimumcostmatching; unbalanced bipartite graph; weightscaling algorithm Call a bipartite graph G = (X; Y;E) balanced when X  = Y . Given a balanced bipartite graph G with edge costs, the assignment problem asks for a perfect matching in G of minimum to ..."
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assignment problem; imperfect matching; minimumcostmatching; unbalanced bipartite graph; weightscaling algorithm Call a bipartite graph G = (X; Y;E) balanced when X  = Y . Given a balanced bipartite graph G with edge costs, the assignment problem asks for a perfect matching in G of minimum total cost. The Hungarian Method can solve assignment problems in time O(mn+n 2 log n), where n: = X  = Y  and m: = E. If the edge weights are integers bounded in magnitude by C> 1, then algorithms using weight scaling, such as that of Gabow and Tarjan, can lower the time to ( log(nC)). There are important applications in which G is unbalanced, with X  ≠ Y , and we require a mincost matching in G of size r: = min(X, Y ) or, more generally, of some specified size s ≤ r. The Hungarian Method extends easily to find such a matching in time O(ms+s 2 log r), but weightscaling algorithms do not extend so easily. We introduce new machinery that allows us to find such a matching in time ( log(nC)) via weight scaling. Our results also provide insight into the design space of efficient weightscaling matching algorithms. These ideas are presented in greater depth in HPL201240 [17].
Licensed under a Creative Commons Attribution License
, 2010
"... Abstract: Rajeev Motwani was a preeminent theoretical computer scientist of his generation, a technology thought leader, an insightful venture capitalist, and a mentor to some of the most influential entrepreneurs in Silicon Valley in the first decade of the 21st century. This article presents an o ..."
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Abstract: Rajeev Motwani was a preeminent theoretical computer scientist of his generation, a technology thought leader, an insightful venture capitalist, and a mentor to some of the most influential entrepreneurs in Silicon Valley in the first decade of the 21st century. This article presents an overview of Rajeev’s research, and provides a window to his early life and the various influences that shaped his research and professional career—it is a small celebration of his wonderful life and many achievements.
SPECIAL ISSUE IN HONOR OF RAJEEV MOTWANI Regularity Lemmas and Combinatorial Algorithms
, 2010
"... Abstract: We present new combinatorial algorithms for Boolean matrix multiplication (BMM) and preprocessing a graph to answer independent set queries. We give the first asymptotic improvements on combinatorial algorithms for dense BMM in many years, improving on the “Four Russians ” O(n3 /(wlogn)) b ..."
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Abstract: We present new combinatorial algorithms for Boolean matrix multiplication (BMM) and preprocessing a graph to answer independent set queries. We give the first asymptotic improvements on combinatorial algorithms for dense BMM in many years, improving on the “Four Russians ” O(n3 /(wlogn)) bound for machine models with wordsize w. (For a pointer machine, we can set w = logn.) The algorithms utilize notions from Regularity Lemmas for graphs in a novel way. • We give two randomized combinatorial algorithms for BMM. The first algorithm is essentially a reduction from BMM to the Triangle Removal Lemma. The best known bounds for the Triangle Removal Lemma only imply an O ( (n 3 logβ)/(βwlogn) ) time algorithm for BMM where β = (log ⋆ n) δ for some δ> 0, but improvements on the Triangle Removal Lemma would yield corresponding runtime improvements. The second algorithm applies the Weak Regularity Lemma of Frieze and Kannan along with several information compression ideas, running in O ( n 3 (loglogn) 2 /(logn) 9/4)) time with probability exponentially close to 1. When w ≥ logn, it can be implemented in O ( n 3 (loglogn)/(wlogn) 7/6) ) time. Our results immediately imply improved combinatorial methods for CFG parsing, detecting trianglefreeness, and transitive closure. ACM Classification: F.2.2 AMS Classification: 68Q25 Key words and phrases: Boolean matrix multiplication, regularity lemma, combinatorial algorithm,