A Strongly Polynomial Algorithm for Controlled Queues

A Strongly Polynomial Algorithm for Controlled Queues

We consider the problem of computing optimal policies of finite-state finite-action Markov decision processes (MDPs). A reduction to a continuum of constrained MDPs (CMDPs) is presented such that the optimal policies for these CMDPs constitute a path in a graph defined over the deterministic policies. This path contains, in particular, an optimal policy of the original MDP. We present an algori...

Xxa Strongly Polynomial - Time Algorithm for Minimizingsubmodular

This paper presents a combinatorial polynomial-time algorithm for minimizing submod-ular set functions. The algorithm employs a scaling scheme that uses a ow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the largest length of the functio...

Strongly polynomial algorithm for generalized flow maximization

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. The full version is available on arXiv:1307.680...

A strongly polynomial minimum cost circulation algorithm

A Strongly Polynomial Algorithm for the Inverse Shortest Arborescence Problem

In this paper an inverse problem of the weighted shortest arborescence problem is discussed. That is. given a directed graph G and a set of nonnegative costs on its arcs. we need to modify those costs as little as possible to ensure that T, a given (.I-arborescence of G, is the shortest one. It is found that only the cost of T needs modifying. An O(rz”) combinatorial algorithm is then proposed....