Related papers: Approximation Limitations of Pure Dynamic Programm…
Tropical circuits are circuits with Min and Plus, or Max and Plus operations as gates. Their importance stems from their intimate relation to dynamic programming algorithms. The power of tropical circuits lies somewhere between that of…
Many dynamic programming algorithms for discrete 0-1 optimizationproblems are "pure" in that their recursion equations only use min/max and addition operations, and do not depend on actual input weights. The well-known greedy algorithm of…
We give unconditional parameterized complexity lower bounds on pure dynamic programming algorithms - as modeled by tropical circuits - for connectivity problems such as the Traveling Salesperson Problem. Our lower bounds are higher than the…
Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but…
We consider probabilistic circuits working over the real numbers, and using arbitrary semialgebraic functions of bounded description complexity as gates. In particular, such circuits can use all arithmetic operations +, -, x, /,…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients.…
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…
We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input--output pairs of an unknown…
We consider a discrete best approximation problem formulated in the framework of tropical algebra, which deals with the theory and applications of algebraic systems with idempotent operations. Given a set of samples of input and output of…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…