Related papers: The Subset Sum Matching Problem
The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
We explore the idea of automatically crafting a tuning dataset for Statistical Machine Translation (SMT) that makes the hyper-parameters of the SMT system more robust with respect to some specific deficiencies of the parameter tuning…
In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
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…
Submodular function maximization is a fundamental combinatorial optimization problem with plenty of applications -- including data summarization, influence maximization, and recommendation. In many of these problems, the goal is to find a…
This survey revisits classical combinatorial optimization algorithms and extends them to two-stage stochastic models, particularly focusing on client-element problems. We reformulate these problems to optimize element selection under…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…