Related papers: A fixed-parameter tractable algorithm for combinat…
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm…
In the context of fault-detection problems, the objective is to identify all defective items among a set of $n$ binary-state items using the minimum number of tests. The {group testing} paradigm, which allows testing a subset of items in a…
NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers…
Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
Collaborative multi-robot perception provides multiple views of an environment, offering varying perspectives to collaboratively understand the environment even when individual robots have poor points of view or when occlusions are caused…
Effective therapy of complex diseases requires control of highly non-linear complex networks that remain incompletely characterized. In particular, drug intervention can be seen as control of signaling in cellular networks. Identification…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Neural network pruning is a widely used strategy for reducing model storage and computing requirements. It allows to lower the complexity of the network by introducing sparsity in the weights. Because taking advantage of sparse matrices is…
Motivated by the study of genome rearrangements, the NP-hard Minimum Common String Partition problems asks, given two strings, to split both strings into an identical set of blocks. We consider an extension of this problem to unbalanced…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
Designing recommendation systems with limited or no available training data remains a challenge. To that end, a new combinatorial optimization problem is formulated to generate optimized item selection for experimentation with the goal to…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinatorial designs which simultaneously provide a generalization…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
Iterative pruning is one of the most effective compression methods for pre-trained language models. We discovered that finding the optimal pruning decision is an equality-constrained 0-1 Integer Linear Programming problem. The solution to…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Randomized experiments have been critical tools of decision making for decades. However, subjects can show significant heterogeneity in response to treatments in many important applications. Therefore it is not enough to simply know which…