We present a formalization of flow networks and the Min-Cut-MaxFlow theorem. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL— the interactive theorem prover used for the formalization.

We consider some inverse min-max (or max-min) network problems. Such an inverse problem is to modify the weights with bound constraints so that a given feasible solution becomes an optimal solution of a min-max (or max-min) network problem, and the deviation of the weights, measured by the weighted l1 norm or weighted l∞ norm, is minimum. In this paper, we present strongly polynomial time algor...

We define the min-min expectation selection problem (resp. max-min expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value resulting when independent random variables are drawn from the selected distributions. We assume each distribution has finitely many atoms. Let d be the num...

Performance of cooperative diversity schemes at Low Signal to Noise Ratios (LSNR) was recently studied by Avestimehr et. al. [1] who emphasized the importance of diversity gain over multiplexing gain at low SNRs. It has also been pointed out that continuous energy transfer to the channel is necessary for achieving the max-flow min-cut bound at LSNR. Motivated by this we propose the use of Selec...

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. Although some aspects generalize , surprising counterexamples are found. We speculate that the phenomena revealed may be of interest in both spin systems in condensed matter and in quantum gravity.

Large-scale projects often have several activities which are performed by subcontractors with limited multi-resources. Project scheduling with limited resources is one of the most famous problems in the research operations and optimization cases. The resource-constraint project scheduling problem (RCPSP) is a NP-hard problem in which the activities of a project must be scheduled to reduce the p...

It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for k-commodity flow instances with arbitrary capacities and demands. This improves upon the previously best-known bound of O(log k) and is existentially tight, up to a constant factor. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus...

Max-min is an established fairness criteria for allocating bandwidth for flows. In this work we look at the combined problem of routing and bandwidth allocation such that the flow allocation for each connection will be maximized and fairness will be maintained. We use the weighted extension of the max-min criteria to allocate bandwidth proportionaly to the flows’ demand. Our contribution is an ...

The embedding of finite metrics in �1 has become a fundamental tool for both combinatorial optimization and largescale data analysis. One important application is to network flow problems as there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into �1. Here we show that this theory can be generalized to a larger set of combinatorial optimiza...

Wireless sensor networks with multiple users collecting data directly from the sensors have many potential applications. An important problem is to allocate for each user a query range to achieve certain global optimality while avoid congesting the sensors in the meanwhile. We study this problem for a ZigBee cluster tree by formulating it into a multi-dimensional multi-choice knapsack problem. ...