257 research outputs found
A simple min cut algorithm
We present an algorithm for finding the minimum cut of an edge-weighted graph.
It is simple in every respect. It has a short and compact description, is easy
to implement and has a surprisingly simple proof of correctness. Its runtime
matches that of the fastest algorithm known. The runtime analysis is
straightforward. In contrast to nearly all approaches so far, the algorithm
uses no flow techniques. Roughly spoken the algorithm consists of about |V|
nearly identical phases each of which is formally similar to Prim's minimum
spanning tree algorithm
Almost-Tight Distributed Minimum Cut Algorithms
We study the problem of computing the minimum cut in a weighted distributed
message-passing networks (the CONGEST model). Let be the minimum cut,
be the number of nodes in the network, and be the network diameter. Our
algorithm can compute exactly in time. To the best of our knowledge, this is the first paper that
explicitly studies computing the exact minimum cut in the distributed setting.
Previously, non-trivial sublinear time algorithms for this problem are known
only for unweighted graphs when due to Pritchard and
Thurimella's -time and -time algorithms for
computing -edge-connected and -edge-connected components.
By using the edge sampling technique of Karger's, we can convert this
algorithm into a -approximation -time algorithm for any . This improves
over the previous -approximation -time algorithm and
-approximation -time algorithm of Ghaffari and Kuhn. Due to the lower
bound of by Das Sarma et al. which holds for any
approximation algorithm, this running time is tight up to a factor.
To get the stated running time, we developed an approximation algorithm which
combines the ideas of Thorup's algorithm and Matula's contraction algorithm. It
saves an factor as compared to applying Thorup's tree
packing theorem directly. Then, we combine Kutten and Peleg's tree partitioning
algorithm and Karger's dynamic programming to achieve an efficient distributed
algorithm that finds the minimum cut when we are given a spanning tree that
crosses the minimum cut exactly once
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Distributed consensus and other linear systems with system stochastic
matrices emerge in various settings, like opinion formation in social
networks, rendezvous of robots, and distributed inference in sensor networks.
The matrices are often random, due to, e.g., random packet dropouts in
wireless sensor networks. Key in analyzing the performance of such systems is
studying convergence of matrix products . In this paper, we
find the exact exponential rate for the convergence in probability of the
product of such matrices when time grows large, under the assumption that
the 's are symmetric and independent identically distributed in time.
Further, for commonly used random models like with gossip and link failure, we
show that the rate is found by solving a min-cut problem and, hence, easily
computable. Finally, we apply our results to optimally allocate the sensors'
transmission power in consensus+innovations distributed detection
Mirroring Mobile Phone in the Clouds
This paper presents a framework of Mirroring Mobile Phone in the Clouds (MMPC) to speed up data/computing intensive applications on a mobile phone by taking full advantage of the super computing power of the clouds. An application on the mobile phone is dynamically partitioned in such a way that the heavy-weighted part is always running on a mirrored server in the clouds while the light-weighted part remains on the mobile phone. A performance improvement (an energy consumption reduction of 70% and a speed-up of 15x) is achieved at the cost of the communication overhead between the mobile phone and the clouds (to transfer the application codes and intermediate results) of a desired application. Our original contributions include a dynamic profiler and a dynamic partitioning algorithm compared with traditional approaches of either statically partitioning a mobile application or modifying a mobile application to support the required partitioning
Adaptive online deployment for resource constrained mobile smart clients
Nowadays mobile devices are more and more used as a platform for applications. Contrary to prior generation handheld devices configured with a predefined set of applications, today leading edge devices provide a platform for flexible and customized application deployment. However, these applications have to deal with the limitations (e.g. CPU speed, memory) of these mobile devices and thus cannot handle complex tasks. In order to cope with the handheld limitations and the ever changing device context (e.g. network connections, remaining battery time, etc.) we present a middleware solution that dynamically offloads parts of the software to the most appropriate server. Without a priori knowledge of the application, the optimal deployment is calculated, that lowers the cpu usage at the mobile client, whilst keeping the used bandwidth minimal. The information needed to calculate this optimum is gathered on the fly from runtime information. Experimental results show that the proposed solution enables effective execution of complex applications in a constrained environment. Moreover, we demonstrate that the overhead from the middleware components is below 2%
Symmetric Submodular Function Minimization Under Hereditary Family Constraints
We present an efficient algorithm to find non-empty minimizers of a symmetric
submodular function over any family of sets closed under inclusion. This for
example includes families defined by a cardinality constraint, a knapsack
constraint, a matroid independence constraint, or any combination of such
constraints. Our algorithm make oracle calls to the submodular
function where is the cardinality of the ground set. In contrast, the
problem of minimizing a general submodular function under a cardinality
constraint is known to be inapproximable within (Svitkina
and Fleischer [2008]).
The algorithm is similar to an algorithm of Nagamochi and Ibaraki [1998] to
find all nontrivial inclusionwise minimal minimizers of a symmetric submodular
function over a set of cardinality using oracle calls. Their
procedure in turn is based on Queyranne's algorithm [1998] to minimize a
symmetric submodularComment: 13 pages, Submitted to SODA 201
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