scholarly journals Improved Strongly Polynomial Algorithms for Deterministic MDPs, 2VPI Feasibility, and Discounted All-Pairs Shortest Paths

2022 ◽  
pp. 154-172
Author(s):  
Adam Karczmarz
Keyword(s):  
Shortest Paths ◽  
Polynomial Algorithms ◽  
Strongly Polynomial Algorithms ◽  
All Pairs Shortest Paths ◽  
Strongly Polynomial

scholarly journals Weakly and strongly polynomial algorithms for computing the maximum decrease in uniform arc capacities

2016 ◽  
Vol 26 (2) ◽  
pp. 159-171
Author(s):  
Mehdi Ghiyasvand
Keyword(s):  
Polynomial Time ◽  
Maximum Flow ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Polynomial Algorithms ◽  
Directed Network ◽  
Strongly Polynomial Algorithms ◽  
Maximum Decrease ◽  
Strongly Polynomial

In this paper, a new problem on a directed network is presented. Let D be a feasible network such that all arc capacities are equal to U. Given a t > 0, the network D with arc capacities U - t is called the t-network. The goal of the problem is to compute the largest t such that the t-network is feasible. First, we present a weakly polynomial time algorithm to solve this problem, which runs in O(log(nU)) maximum flow computations, where n is the number of nodes. Then, an O(m2n) time approach is presented, where m is the number of arcs. Both the weakly and strongly polynomial algorithms are inspired by McCormick and Ervolina (1994).

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