Related papers: Translationally Invariant Constraint Optimization …
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input.…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
Neural networks (NNs) have emerged as powerful tools for solving high-dimensional optimal control problems. In particular, their compositional structure has been shown to enable efficient approximation of high-dimensional functions, helping…
Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise,…
Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…
We prove that any perfect quantum strategy for the two-prover game encoding a constraint satisfaction problem (CSP) can be simulated via a perfect classical strategy with an extra classical communication channel, whose size depends only on…
An important problem that commonly arises in areas such as internet traffic-flow analysis, phylogenetics and electrical circuit design, is to find a representation of any given metric $D$ on a finite set by an edge-weighted graph, such that…
We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…
The optimal transmission switching problem (OTSP) is an established problem of changing a power grid's topology to obtain an improved operation by controlling the switching status of transmission lines. This problem was proven to be…
We study the complexity of SAT($\Gamma$) problems for potentially infinite languages $\Gamma$ closed under variable negation (sign-symmetric languages). Via an algebraic connection, this reduces to the study of restricted partial…
We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrised version of the classical fidelity). These are crucial for establishing global linear…
What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…
Classically, for many computational problems one can conclude time lower bounds conditioned on the hardness of one or more of key problems: k-SAT, 3SUM and APSP. More recently, similar results have been derived in the quantum setting…
The article considers one of the possible generalizations of constraint satisfaction problems where relations are replaced by multivalued membership functions. In this case operations of disjunction and conjunction are replaced by maximum…
In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains…
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…
We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space…
We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…