Related papers: On the Fine-Grained Complexity of Parity Problems
A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such…
A lot of theoretical and empirical evidence shows that the flatter local minima tend to improve generalization. Adversarial Weight Perturbation (AWP) is an emerging technique to efficiently and effectively find such minima. In AWP we…
Given an undirected graph $G=(V,E)$ and an integer $\ell$, the Eccentricity Shortest Path (ESP) asks to find a shortest path $P$ such that for every vertex $v\in V(G)$, there is a vertex $w\in P$ such that $d_G(v,w)\leq \ell$, where…
Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…
In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…
We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence…
We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. Our reductions can be applied to both exact and approximate…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
In recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower…
We present a very simple and intuitive algorithm to find balanced sparse cuts in a graph via shortest-paths. Our algorithm combines a new multiplicative-weights framework for solving unit-weight multi-commodity flows with standard ball…
We study the complexity of approximating solution structure of the bijective weighted sentence alignment problem of DeNero and Klein (2008). In particular, we consider the complexity of finding an alignment that has a significant overlap…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…
The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in the other part.…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases -…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
We investigate parameterized algorithms for the NP-hard problem Min-Power Asymmetric Connectivity (MinPAC) that has applications in wireless sensor networks. Given a directed arc-weighted graph, MinPAC asks for a strongly connected spanning…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…