On Vegh's Strongly Polynomial Algorithm for Generalized Flows [PDF]
, 2014 This thesis contains an exposition of the new strongly polynomial algorithm for the generalized flow problem by Laszlo Vegh (2013). It has been a long-standing open question whether such an algorithm exists, until it was resolved by Vegh in 2013 ...
Lo, Venus Hiu Ling
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Hardness of submodular cost allocation : lattice matching and a simplex coloring conjecture [PDF]
, 2014 We consider the Minimum Submodular Cost Allocation (MSCA) problem. In this problem, we are given k submodular cost functions f1, ... , fk: 2V -> R+ and the goal is to partition V into k sets A1, ..., Ak so as to minimize the total cost sumi = 1,k fi(Ai).
Vondrák, Jan, Ene, Alina
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A strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives [PDF]
, 2016 A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E}C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function.
Végh, László A.
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Strongly polynomial frame scaling to high precision [PDF]
The frame scaling problem is: given vectors U := {u1, ..., un} ⊆ Rd, marginals c ∈ Rn++, and precision ε > 0, find left and right scalings L ∈ Rd×d, r ∈ Rn++ such that (v1, ..., vn):= (Lu1r1, ..., Lunrn) simultaneously satisfies (Equation presented) and ∥
Ramachandran, A. (Akshay) +1 more
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The Two Variable Per Inequality Abstract Domain [PDF]
, 2010 This article presents the Two Variable Per Inequality abstract domain (TVPI domain for short). This so-called weakly-relational domain is able to express systems of linear inequalities where each inequality has at most two variables.
Howe, Jacob M., Simon, Axel, King, Andy
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A strongly polynomial-time algorithm for minimizing submodular functions [PDF]
This paper presents a combinatorial polynomial-time algorithm for minimizing submolular set functions. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to thescaled ...
IWATA, Satoru +2 more
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The existence of a strongly polynomial time simplex algorithm for linear programs [PDF]
, 2022 It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs).
Yan, Zi-zong, Guo, Jinhai, Li, Xiang-jun
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Strongly polynomial-time truthful mechanisms in one shot [PDF]
, 2009 One of the main challenges in algorithmic mechanism design is to turn (existing) efficient algorithmic solutions into efficient truthful mechanisms. Building a truthful mechanism is indeed a difficult process since the underlying algorithm must obey ...
P. PENNA +4 more
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A strongly polynomial algorithm for the Balanced network flow problem [PDF]
, 1999 We show that the Balanced Network Flow Problem in the case of general weights, i.e., the problem of finding a feasible flow on a given network which minimizes the difference between the maximum and the minimum weighted flow on single arcs, can be ...
Bettina, Klinz +3 more
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On strongly polynomial variants of the MBU-simplex algorithm for a maximum flow problem with non-zero lower bounds [PDF]
, 2014 In this paper, we are concerned with maximum flow problems with non-zero lower bounds. The common approach to this problem is transforming the network into a bigger one with zero lower bounds, whose optimal solution yields a feasible solution to the ...
Molnár-Szipai, Richárd, Illés, Tibor
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