5,905 research outputs found
Speeding Up the Estimation of Expected Maximum Flows Through Reliable Networks
In this paper we present a strategy for speeding up the estimation of expected maximum flows through reliable networks. Our strategy tries to minimize the repetition of computational effort while evaluating network states sampled using the crude Monte Carlo method. Computational experiments with this strategy on three types of randomly generated networks show that it reduces the number of flow augmentations required for evaluating the states in the sample by as much as 52% on average with a standard deviation of 7% compared to the conventional strategy. This leads to an average time saving of about 71% with a standard deviation of about 8%.
Maximum Skew-Symmetric Flows and Matchings
The maximum integer skew-symmetric flow problem (MSFP) generalizes both the
maximum flow and maximum matching problems. It was introduced by Tutte in terms
of self-conjugate flows in antisymmetrical digraphs. He showed that for these
objects there are natural analogs of classical theoretical results on usual
network flows, such as the flow decomposition, augmenting path, and max-flow
min-cut theorems. We give unified and shorter proofs for those theoretical
results.
We then extend to MSFP the shortest augmenting path method of Edmonds and
Karp and the blocking flow method of Dinits, obtaining algorithms with similar
time bounds in general case. Moreover, in the cases of unit arc capacities and
unit ``node capacities'' the blocking skew-symmetric flow algorithm has time
bounds similar to those established in Even and Tarjan (1975) and Karzanov
(1973) for Dinits' algorithm. In particular, this implies an algorithm for
finding a maximum matching in a nonbipartite graph in time,
which matches the time bound for the algorithm of Micali and Vazirani. Finally,
extending a clique compression technique of Feder and Motwani to particular
skew-symmetric graphs, we speed up the implied maximum matching algorithm to
run in time, improving the best known bound
for dense nonbipartite graphs.
Also other theoretical and algorithmic results on skew-symmetric flows and
their applications are presented.Comment: 35 pages, 3 figures, to appear in Mathematical Programming, minor
stylistic corrections and shortenings to the original versio
Computational investigations of maximum flow algorithms
"April 1995."Includes bibliographical references (p. 55-57).by Ravindra K. Ahuja ... [et al.
New distance-directed algorithms for maximum flow and parametric maximum flow problems
"July 1987."Bibliography: p. 34-36.Supported, in part, by the Presidential Young Investigator Grant of the National Science Foundation. 8451517-ECS Supported, in part, by a grant from Analog Devices, Apple Computer,Inc., and Prime Computer.J. B. Orlin and Ravindra K. Ahuja
Weighted Matchings via Unweighted Augmentations
We design a generic method for reducing the task of finding weighted
matchings to that of finding short augmenting paths in unweighted graphs. This
method enables us to provide efficient implementations for approximating
weighted matchings in the streaming model and in the massively parallel
computation (MPC) model.
In the context of streaming with random edge arrivals, our techniques yield a
-approximation algorithm thus breaking the natural barrier of .
For multi-pass streaming and the MPC model, we show that any algorithm
computing a -approximate unweighted matching in bipartite graphs
can be translated into an algorithm that computes a
-approximate maximum weighted matching. Furthermore,
this translation incurs only a constant factor (that depends on ) overhead in the complexity. Instantiating this with the current best
multi-pass streaming and MPC algorithms for unweighted matchings yields the
following results for maximum weighted matchings:
* A -approximation streaming algorithm that uses
passes and memory.
This is the first -approximation streaming algorithm for
weighted matchings that uses a constant number of passes (only depending on
).
* A -approximation algorithm in the MPC model that uses
rounds, machines per round, and
memory per machine. This improves upon
the previous best approximation guarantee of for weighted
graphs
Faster Algorithms for Semi-Matching Problems
We consider the problem of finding \textit{semi-matching} in bipartite graphs
which is also extensively studied under various names in the scheduling
literature. We give faster algorithms for both weighted and unweighted case.
For the weighted case, we give an -time algorithm, where is
the number of vertices and is the number of edges, by exploiting the
geometric structure of the problem. This improves the classical
algorithms by Horn [Operations Research 1973] and Bruno, Coffman and Sethi
[Communications of the ACM 1974].
For the unweighted case, the bound could be improved even further. We give a
simple divide-and-conquer algorithm which runs in time,
improving two previous -time algorithms by Abraham [MSc thesis,
University of Glasgow 2003] and Harvey, Ladner, Lov\'asz and Tamir [WADS 2003
and Journal of Algorithms 2006]. We also extend this algorithm to solve the
\textit{Balance Edge Cover} problem in time, improving the
previous -time algorithm by Harada, Ono, Sadakane and Yamashita [ISAAC
2008].Comment: ICALP 201
Cut Tree Construction from Massive Graphs
The construction of cut trees (also known as Gomory-Hu trees) for a given
graph enables the minimum-cut size of the original graph to be obtained for any
pair of vertices. Cut trees are a powerful back-end for graph management and
mining, as they support various procedures related to the minimum cut, maximum
flow, and connectivity. However, the crucial drawback with cut trees is the
computational cost of their construction. In theory, a cut tree is built by
applying a maximum flow algorithm for times, where is the number of
vertices. Therefore, naive implementations of this approach result in cubic
time complexity, which is obviously too slow for today's large-scale graphs. To
address this issue, in the present study, we propose a new cut-tree
construction algorithm tailored to real-world networks. Using a series of
experiments, we demonstrate that the proposed algorithm is several orders of
magnitude faster than previous algorithms and it can construct cut trees for
billion-scale graphs.Comment: Short version will appear at ICDM'1
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