We study the maximum flow problem in directed H-minorfree graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a clique-sum of planar graphs and graphs of constant complexity is given, we show that a maximum flow can be computed in O(n logn) time. In particular, maximum flows in directed K3,3-minor-free graphs and directed K5-minor-free graph...

In the present work an attempt is being made to reduce the Maximum Flow Network Interdiction Problem (MFNIP) in to the Subset Sum Problem so as to get some algorithms solvable in polynomial time. Previously developed algorithms are either applicable to some special cases of MFNIP or they do not have a constant performance guarantee. Our reduction has paved the way towards the development of ful...

Пусть $X_1,…, X_n $ - независимые случайные величины, принимающие значения в алфавите $\{0,1,…,r\} $, и $S_n=\sum_{i=1}^nX_i$. Теорема Шеппа-Олкина утверждает, что бинарном случае ($r=1$) энтропия Шеннона случайной величины $S_n$ максимальна, когда все $X_i$ равномерно распределены, т.е. являются бернуллиевскими с параметром $1/2$. Стремясь обобщить эту теорему на случай конечных алфавитов, мы ...