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Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
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…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
We consider the robustness of computational hardness of problems whose input is obtained by applying independent random deletions to worst-case instances. For some classical $NP$-hard problems on graphs, such as Coloring, Vertex-Cover, and…
This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…
A standard type of uncertainty set in robust optimization is budgeted uncertainty, where an interval of possible values for each parameter is given and the total deviation from their lower bounds is bounded. In the two-stage setting,…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
The emergence of systems with non-volatile main memory (NVM) increases the interest in the design of \emph{recoverable concurrent objects} that are robust to crash-failures, since their operations are able to recover from such failures by…
Training Deep Neural Networks (DNNs) with adversarial examples often results in poor generalization to test-time adversarial data. This paper investigates this issue, known as adversarially robust generalization, through the lens of…
The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution and the adversary selects costs…
We investigate the complexity of three optimization problems in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…
We propose a model for recoverable robust optimization with commitment. Given a combinatorial optimization problem and uncertainty about elements that may fail, we ask for a robust solution that, after the failing elements are revealed, can…
We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack and the follower chooses an optimal packing according to his own profits, which may differ from those of the leader. To this bilevel…
A significant progress has been made in the past three decades over the study of combinatorial NP optimization problems and their associated optimization and approximate classes, such as NPO, PO, APX (or APXP), and PTAS. Unfortunately, a…
We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems,…