Related papers: CLAP: A New Algorithm for Promise CSPs
We study approximation algorithms for scheduling problems with the objective of minimizing total weighted completion time, under identical and related machine models with job precedence constraints. We give algorithms that improve upon many…
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…
A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…
In this paper we study the computational complexity of the (extended) minimum cost homomorphism problem (Min-Cost-Hom) as a function of a constraint language, i.e. a set of constraint relations and cost functions that are allowed to appear…
We initiate a study of when the value of mathematical relaxations such as linear and semidefinite programs for constraint satisfaction problems (CSPs) is approximately preserved when restricting the instance to a sub-instance induced by a…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…
We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
The Quadratic Assignment Problem (QAP) is an important discrete optimization instance that encompasses many well-known combinatorial optimization problems, and has applications in a wide range of areas such as logistics and computer vision.…
The approximate graph colouring problem, whose complexity is unresolved in most cases, concerns finding a $c$-colouring of a graph that is promised to be $k$-colourable, where $c\geq k$. This problem naturally generalises to promise graph…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…
We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a…
Binary code representation learning has shown significant performance in binary analysis tasks. But existing solutions often have poor transferability, particularly in few-shot and zero-shot scenarios where few or no training samples are…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
Continual learning (CL) aims to help deep neural networks learn new knowledge while retaining what has been learned. Owing to their powerful generalizability, pre-trained vision-language models such as Contrastive Language-Image…
Solving mixed-integer nonlinear programs (MINLPs) typically relies on constructing relaxations that are easier to tackle than the original problem. Recently, global parabolic (PARA) relaxations were introduced, featuring separable quadratic…
This paper studies complete $k$-Constraint Satisfaction Problems (CSPs), where an $n$-variable instance has exactly one nontrivial constraint for each subset of $k$ variables, i.e., it has $\binom{n}{k}$ constraints. A recent work started a…