Related papers: The Complexity Classes of Hamming Distance Recover…
In bilevel and robust optimization we are concerned with combinatorial min-max problems, for example from the areas of min-max regret robust optimization, network interdiction, most vital vertex problems, blocker problems, and two-stage…
Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…
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…
This article deals with the generalization performance of margin multi-category classifiers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures…
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We…
Learning to predict solutions to real-valued combinatorial graph problems promises efficient approximations. As demonstrated based on the NP-hard edge clique cover number, recurrent neural networks (RNNs) are particularly suited for this…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
Flat regions of the neural network loss landscape have long been hypothesized to correlate with better generalization properties. A closely related but distinct problem is training models that are robust to internal perturbations to their…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
An important objective of research in counting complexity is to understand which counting problems are approximable. In this quest, the complexity class TotP, a hard subclass of #P, is of key importance, as it contains self-reducible…
The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We…
Protein structures can be encoded into binary sequences, these are used to define a Hamming distance in conformational space: the distance between two different molecular conformations is the number of different bits in their sequences.…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
The low-degree polynomial framework has emerged as a powerful tool for providing evidence of statistical-computational gaps in high-dimensional inference. For detection problems, the standard approach bounds the low-degree advantage through…
In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a…
We study the general norm optimization for combinatorial problems, initiated by Chakrabarty and Swamy (STOC 2019). We propose a general formulation that captures a large class of combinatorial structures: we are given a set $U$ of $n$…
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…