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This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem(P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of(P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of(P)does not exist, which can be seen as an accelerating device for the solution algorithm of(P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem(P)provided that the number of variables is not too large.

International audience; A minimum cost maximum flow algorithm is proposed for resources (e.g. virtual machines) placement in clouds confronted to dynamic workloads and flows variations. The algorithm is compared to an exact method generalizing the classical Bin-Packing formulation using a linear integer program. A directed graph is used to model the allocation problem for cloud resources organized in a finite number of resource types; a common practice in cloud services. Providers can use the minimum cost maximum flow algorithm to opportunistically select the most appropriate physical resources to serve applications or to ensure elastic platform provisioning. The modified Bin-Packing algorithm is used to benchmark the minimum cost maximum flow solution. The latter combined with a prediction mechanism to handle dynamic variations achieves near optimal performance.

We develop a decomposition algorithm for the quadratic multicommodity network flow problem, using a row-action primal-dual algorithm. The algorithm decomposes the problem first by commodity and then by arc. Hence, it is suitable for parallel implementations. We study two parallelization strategies of this algorithm. These are the “parallelization within a commodity” (PWC) and the “parallelization across commodities” (PAC). Both strategies are evaluated empirically. Extensive computational results indicate that (1) the row-action algorithm is efficient For a wide range of problem characteristics, (2) the algorithm achieves almost linear speedup on a small scale parallel architecture, and (3) the algorithm can solve efficiently very large problems, with up to 4000 nodes, 80000 arcs and 80 commodities.

We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to ‘real-life’ problems show that the algorithm is competitive with the fastest algorithms known so far.

A trust-region algorithm is presented for solving optimization problem with equality constraints. The algorithm uses the Byrd–Omojokun scheme to compute the steps, and decompose the trial steps into two components: normal component and tangential component. But it differs from the Byrd–Omojokun algorithm with a reduced dimension approach in computing each tangential component. Global convergence of the proposed algorithm is proved under some mild assumptions. Three numerical examples are given to illustrate the efficiency of the algorithm.

The space complexity of the maximum flow problem is investigated. It is shown that the problem is log space complete for deterministic polynomial time. Thus the maximum flow problem probably has no algorithm which needs only O(logk n) storage space for any constant k. Another consequence is that there is probably no fast parallel algorithm for the maximum flow problem.

Given an undirected network, the multi-terminal network flows analysis consists in determining the all pairs maximum flow values. In this paper, we consider an undirected network in which some edge capacities are allowed to vary and we analyze the impact of such variations on the all pairs maximum flow values. We first provide an efficient algorithm for the single parametric capacity case, and then propose a generalization to the case of multiple parametric capacities. Moreover, we provide a study on Gomory–Hu cut-tree relationships.

This paper describes an optimal algorithm for searching for a minimum (or a maximum) of a discrete periodic bimodal function of period P. Recursive computing is used to prove the optimality of the search algorithm. An application of the algorithm for a clustering analysis of a data communication network is provided.