Related papers: The Reward-Penalty-Selection Problem
The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to…
The set covering problem (SCP) is one of the representative combinatorial optimization problems, having many practical applications. This paper investigates the development of an algorithm to solve SCP by employing chemical reaction…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…
In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions may influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more…
Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as…
Stochastic sequential decision making often requires hierarchical structure in the problem where each high-level action should be further planned with primitive states and actions. In addition, many real-world applications require a plan…
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…
Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems,…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of…
Policy optimization is among the most popular and successful reinforcement learning algorithms, and there is increasing interest in understanding its theoretical guarantees. In this work, we initiate the study of policy optimization for the…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types…
We study a stochastic single-machine scheduling problem, denoted the Unreliable Job Selection and Sequencing Problem (UJSSP). Given a set of jobs, a subset must be selected for processing on a single machine that is subject to failure. Each…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y…
The Subset Sum Problem is a fundamental NP-complete problem in cryptography and combinatorial optimization, with many real-world applications. The Random Subset Sum Problem (RSSP) is a more applicable version of subset sum, where numbers…
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…