Related papers: The Subset Sum Matching Problem
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
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…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
Entity summarization is the problem of computing an optimal compact summary for an entity by selecting a size-constrained subset of triples from RDF data. Entity summarization supports a multiplicity of applications and has led to fruitful…
Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
We study the classical weighted perfect matchings problem for bipartite graphs or sometimes referred to as the assignment problem, i.e., given a weighted bipartite graph $G = (U\cup V,E)$ with weights $w : E \rightarrow \mathcal{R}$ we are…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
We propose a multi-criteria Composite Index Method (CIM) to compare the performance of alternative approaches to solving an optimization problem. The CIM is convenient in those situations when neither approach dominates the other when…
We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…
In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…