Related papers: The devil is in Asymmetries (Rough Version)
We introduce the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K. This natural problem applies to…
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…
We observe that the vocabulary used to construct the "answer" to problems in computer algebra can have a dramatic effect on the computational complexity of solving that problem. We recall a formalization of this observation and explain the…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
We study the computational complexity of some explainable clustering problems in the framework proposed by [Dasgupta et al., ICML 2020], where explainability is achieved via axis-aligned decision trees. We consider the $k$-means,…
We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance…
We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs by two methods: one by time discretisation through elliptic…
We study systems of String Equations where block variables need to be assigned strings so that their concatenation gives a specified target string. We investigate this problem under a multivariate complexity framework, searching for…
We consider the possibility problem of determining if a document is a possible world of a probabilistic document, in the setting of probabilistic XML. This basic question is a special case of query answering or tree automata evaluation, but…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
The solving degree of a system of multivariate polynomial equations provides an upper bound for the complexity of computing the solutions of the system via Groebner bases methods. In this paper, we consider polynomial systems that are…
In connection with machine arithmetic, we are interested in systems of constraints of the form x + k \leq y + k'. Over integers, the satisfiability problem for such systems is polynomial time. The problem becomes NP complete if we restrict…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…