Experimental study of minimum cut algorithms

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. [123]-126).by Matthew S. Levine.M.S

Local Search Approximation Algorithms for Clustering Problems

In this research we study the use of local search in the design of approximation algorithms for NP-hard optimization problems. For our study we have selected several well-known clustering problems: k-facility location problem, minimum mutliway cut problem, and constrained maximum k-cut problem. We show that by careful use of the local optimality property of the solutions produced by local search algorithms it is possible to bound the ratio between solutions produced by local search approximation algorithms and optimum solutions. This ratio is known as the locality gap. The locality gap of our algorithm for the k-uncapacitated facility location problem is 2+sqrt(3) +epsilon for any constant epsilon \u3e0. This matches the approximation ratio of the best known algorithm for the problem, proposed by Zhang but our algorithm is simpler. For the minimum multiway cut problem our algorithm has locality gap 2-2/k, which matches the approximation ratio of the isolation heuristic of Dahlhaus et al; however, our experimental results show that in practice our local search algorithm greatly outperforms the isolation heuristic, and furthermore it has comparable performance as that of the three currently best algorithms for the minimum multiway cut problem. For the constrained maximum k-cut problem on hypergraphs we proposed a local search based approximation algorithm with locality gap 1-1/k for a variety of constraints imposed on the k-cuts. The locality gap of our algorithm matches the approximation ratio of the best known algorithm for the max k-cut problem on graphs designed by Vazirani, but our algorithm is more general

Practical Minimum Cut Algorithms

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability

Optimization of Cutting Parameters for Cutting Force in Shoulder Milling of Al7075-T6 Using Response Surface Methodology and Genetic Algorithm

AbstractThis paper aims at developing a statistical model to predict cutting force in terms of machining parameters such as cutting speed, cutting feed rate and axial depth of cut. Response surface methodology experimental design was used for conducting experiments. The work piece material was Aluminum (Al 7075-T6) and the tool was a shoulder mill with two carbide insert. The cutting forces were measured using three axis milling tool dynamometer. The second order mathematical model in terms of machining parameters was developed for predicting cutting force. The adequacy of the predictive models was tested by analysis of variance and found to be adequate. The direct and interaction effect was graphically plotted which helps to study the significance of these parameters with cutting force. The optimization of shoulder mill machining parameters to acquire minimum cutting force was done by genetic algorithms (GA). A Matlab genetic algorithm solver was used to do the optimization

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 $n$ times, where $n$ 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