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We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one source/sink pair among the n distinguished source/sink pairs at a time and treat the given multicommodity network as a single commodity network for such chosen source/sink pair. Then applying standard labeling algorithm, separately for each sink/source pair, the feasible flow which is max flow and the corresponding minimum cut corresponding to each source/sink pair is obtained. A record is made of these cuts and the paths flowing through the edges of these cuts. This record is then utilized to develop our algorithm to obtain max flow for multicommodity flow. In this paper we have pinpointed the difficulty behind not getting a max flow min cut type theorem for multicommodity flow and found out a remedy.
In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.
When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The conventional
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea of our ap
The aim of this paper is to provide a new class of series identities in the form of four general results. The results are established with the help of generalizatons of the classical Kummers summation theorem obtained earlier by Rakha and Rathie. Res