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Finding Maximum Degrees in Hidden Bipartite Graphs
, 2010
"... An (edge) hidden graph is a graph whose edges are not explicitly given. Detecting the presence of an edge requires expensive edgeprobing queries. We consider thek most connected vertex problem on hidden bipartite graphs. Specifically, given a bipartite graph G with independent vertex sets B and W, t ..."
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Cited by 2 (0 self)
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An (edge) hidden graph is a graph whose edges are not explicitly given. Detecting the presence of an edge requires expensive edgeprobing queries. We consider thek most connected vertex problem on hidden bipartite graphs. Specifically, given a bipartite graph G with independent vertex sets B and W
Finding Maximum Edge Bicliques in Convex Bipartite Graphs?
"... Abstract. A bipartite graph G = (A,B,E) is convex on B if there exists an ordering of the vertices of B such that for any vertex v ∈ A, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. Motivated by an application to analyzing DNA mic ..."
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microarray data, we study the problem of finding maximum edge bicliques in convex bipartite graphs. Given a bipartite graph G = (A,B,E) which is convex on B, we present a new algorithm that computes a maximum edge biclique of G in O(n log3 n log log n) time and O(n) space, where n = A. This improves
On Packing Bipartite Graphs
"... G and H, two simple graphs, can be packed if G is isomorphic to a subgraph of H, the complement of H. A theorem of Catlin, Spencer and Sauer gives a sufficient condition for the existence of packing in terms of the product of the maximal degrees of G and H. We improve this theorem for bipartite gra ..."
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graphs. Our condition involves products of a maximum degree with an average degree. Our relaxed condition still guarantees a packing of the two bipartite graphs.
The Complexity of Counting in Sparse, Regular, and Planar Graphs
 SIAM Journal on Computing
, 1997
"... We show that a number of graphtheoretic counting problems remain NPhard, indeed #Pcomplete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to ..."
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Cited by 88 (0 self)
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We show that a number of graphtheoretic counting problems remain NPhard, indeed #Pcomplete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted
Clustering of Bipartite AdvertiserKeyword Graph
, 2003
"... In this paper we present topdown and bottomup hierarchical clustering methods for large bipartite graphs. The top down approach employs a flowbased graph partitioning method, while the bottom up approach is a multiround hybrid of the singlelink and averagelink agglomerative clustering methods. ..."
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Cited by 24 (1 self)
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In this paper we present topdown and bottomup hierarchical clustering methods for large bipartite graphs. The top down approach employs a flowbased graph partitioning method, while the bottom up approach is a multiround hybrid of the singlelink and averagelink agglomerative clustering methods
On Advice Complexity of the kserver Problem under Sparse Metrics
"... Abstract. We consider the kServer problem under the advice model of computation when the underlying metric space is sparse. On one side, we show that an advice of size Ω(n) is required to obtain a 1competitive algorithm for sequences of size n, even for the 2server problem on a path metric of siz ..."
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of size N ≥ 5. Through another lower bound argument, we show that at least n 2 (logα − 1.22) bits of advice is required to obtain an optimal solution3 for metric spaces of treewidth α, where 4 ≤ α < 2k. On the other side, we introduce Θ(1)competitive algorithms for a wide range of sparse graphs, which
Hamiltonian Cycles in Sparse Graphs
, 2004
"... The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle within a graph is a simple cycle that pas ..."
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The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle within a graph is a simple cycle
Distance oracles for sparse graphs
 In Proceedings of the 50th IEEE Symposium on Foundations of Computer Science (FOCS
"... Abstract — Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer k, they showed an efficient algorithm to construct an approximate distance oracle using space O(kn 1+1/k) that can answe ..."
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Cited by 26 (4 self)
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, then the space complexity is at least n 1+1/k. Their proof holds even if infinite query time is allowed: it is essentially an “incompressibility ” result. Also, the proof only holds for dense graphs, and the best bound it can prove only implies that the size of the data structure is lower bounded by the number
Results 1  10
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