Cut Tree Algorithms: An Experimental Study

Goldberg, Andrew V.; Tsioutsiouliklis, Kostas

doi:10.1006/jagm.2000.1136

Cited by 52 publications

(33 citation statements)

References 14 publications

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“…In [9], the authors experimentally compared different approaches for constructing mincut trees. In our work, we use the GHs implementation (a variant of the Gomory-Hu algorithm [22] using the source selection heuristic) because it turned out to be more robust than other codes [9].…”

Section: Minctcmentioning

confidence: 99%

Collusion Detection for Grid Computing

Staab

Engel

2009

2009 9th IEEE/ACM International Symposium on Cluster Computing and the Grid

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A common technique for result verification in grid computing is to delegate a computation redundantly to different workers and apply majority voting to the returned results. However, the technique is sensitive to "collusion" where a majority of malicious workers collectively returns the same incorrect result. In this paper, we propose a mechanism that identifies groups of colluding workers. The mechanism is based on the fact that colluders can succeed in a vote only when they hold the majority. This information allows us to build clusters of workers that voted similarly in the past, and so detect collusion. We find that the more strongly workers collude, the better they can be identified.

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Section: Minctcmentioning

confidence: 99%

Collusion Detection for Grid Computing

Staab

Engel

2009

2009 9th IEEE/ACM International Symposium on Cluster Computing and the Grid

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“…(i) To all vertices v V , connect an artificial sink vertex t with an edge weight of˛, that is, w.vt/ D˛. Let H be the extended graph of G, after connecting t to all vertices in G. (ii) Using the Gomory-Hu minimum cut tree formation algorithm [20], compute the minimum cut tree T H of the graph H . (iii) Delete the sink vertex t from the cut tree T H to obtain a forest of trees say Trees.T H /.…”

Section: Cut Clustering Algorithmmentioning

confidence: 99%

Parallelization of a graph‐cut based algorithm for hierarchical clustering of web documents

Seshadri¹,

Shalinie²

2015

Concurrency and Computation

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SUMMARYWe propose a parallelization scheme for an existing algorithm for constructing a web-directory, that contains categories of web documents organized hierarchically. The clustering algorithm automatically infers the number of clusters using a quality function based on graph cuts. A parallel implementation of the algorithm has been developed to run on a cluster of multi-core processors interconnected by an intranet. The effect of the well-known Latent Semantic Indexing on the performance of the clustering algorithm is also considered. The parallelized graph-cut based clustering algorithm achieves an F-measure in the range OE0:69; 0:91 for the generated leaf-level clusters while yielding a precision-recall performance in the range OE0:66; 0:84 for the entire hierarchy of the generated clusters. As measured via empirical observations, the parallel algorithm achieves an average speedup of 7.38 over its sequential variant, at the same time yielding a better clustering performance than the sequential algorithm in terms of F-measure.

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“…Formally, A cut-equivalent tree to a graph G is an edge-capacitated tree T on the same set of nodes, with the property that for every pair of nodes s, t, every minimum st-cut in T yields a bipartition of the nodes which is a minimum st-cut in G, and of the same value as in T . 3 See also [GT01] for an experimental study, and the Encyclopedia of Algorithms [Pan16] for more background. The only algorithm that constructs a cut-equivalent tree without making Ω(n) calls to a Max-Flow algorithm was designed by Bhalgat, Hariharan, Kavitha, and Panigrahi [BHKP07].…”

Section: Introductionmentioning

confidence: 99%

New Algorithms and Lower Bounds for All-Pairs Max-Flow in Undirected Graphs

Abboud¹,

Krauthgamer²,

Trabelsi³

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with n nodes and m edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair s, t) can be solved in time T (m), then an O(n 2 ) · T (m) is a trivial upper bound. But can we do better?For directed graphs, recent results in fine-grained complexity suggest that this time bound is essentially optimal. In contrast, for undirected graphs with edge capacities, a seminal algorithm of Gomory and Hu (1961) runs in much faster time O(n)·T (m). Under the plausible assumption that Max-Flow can be solved in near-linear time m 1+o(1) , this half-century old algorithm yields an nm 1+o(1) bound. Several other algorithms have been designed through the years, including O(mn) time for unit-capacity edges (unconditionally), but none of them break the O(mn) barrier. Meanwhile, no super-linear lower bound was shown for undirected graphs.We design the first hardness reductions for All-Pairs Max-Flow in undirected graphs, giving an essentially optimal lower bound for the node-capacities setting. For edge capacities, our efforts to prove similar lower bounds have failed, but we have discovered a surprising new algorithm that breaks the O(mn) barrier for graphs with unit-capacity edges! Assuming T (m) = m 1+o(1) , our algorithm runs in time m 3/2+o(1) and outputs a cut-equivalent tree (similarly to the Gomory-Hu algorithm). Even with current Max-Flow algorithms we improve state-of-the-art as long as m = O(n 5/3−ε ). Finally, we explain the lack of lower bounds by proving a non-reducibility result. This result is based on a new quasi-linear timeÕ(m) non-deterministic algorithm for constructing a cut-equivalent tree and may be of independent interest. * A full version appears at arXiv:1901.01412 † 1 Throughout, we focus on computing the value of the flow (rather than an actual flow), which is equal to the value of the minimum st-cut by the famous max-flow/min-cut theorem [FF56].2 SETH asserts that for every fixed ε > 0 there is an integer k ≥ 3, such that kSAT on n variables and m clauses cannot be solved in time 2 (1−ε)n m O(1) .3 Notice that a minimum st-cut in T consists of a single edge that has minimum capacity along the unique st-path in T , and removing this edge disconnects T to two connected components. A flow-equivalent tree has the weaker property that for every pair of nodes s, t, the maximum st-flow value in T equals that in G. The key difference is that flow-equivalence maintains only the values of the flows (and thus also of the corresponding cuts).

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Cut Tree Algorithms: An Experimental Study

Cited by 52 publications

References 14 publications

Collusion Detection for Grid Computing

Collusion Detection for Grid Computing

Parallelization of a graph‐cut based algorithm for hierarchical clustering of web documents

New Algorithms and Lower Bounds for All-Pairs Max-Flow in Undirected Graphs

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