Related papers: End of Potential Line
We study functions $f : [0, 1]^d \rightarrow [0, 1]^d$ that are both monotone and contracting, and we consider the problem of finding an $\varepsilon$-approximate fixed point of $f$. We show that the problem lies in the complexity class…
Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In \cite{carmeli2020} (\textsc{Pods 2017}) Carmeli \emph{et al.}…
The problem of constrained reinforcement learning (CRL) holds significant importance as it provides a framework for addressing critical safety satisfaction concerns in the field of reinforcement learning (RL). However, with the introduction…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Constrained Optimum Path (COP) problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
We present a new algorithm for finding an $\epsilon$-approximate fixed point of an $\ell_\infty$-contracting function $f : [0, 1]^d \rightarrow [0, 1]^d$. Our algorithm is based on the query-efficient algorithm by Chen, Li, and Yannakakis…
Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal…
Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher…
Klaus showed that the Oriented Matroid Complementarity Problem (OMCP) can be solved by a reduction to the problem of sink-finding in a unique sink orientation (USO) if the input is promised to be given by a non-degenerate extension of a…
Unconstrained Online Linear Optimization (OLO) is a practical problem setting to study the training of machine learning models. Existing works proposed a number of potential-based algorithms, but in general the design of these potential…
With the rapid popularization of big data, the dichotomy between tractable and intractable problems in big data computing has been shifted. Sublinear time, rather than polynomial time, has recently been regarded as the new standard of…
We give an algorithm for finding an $\epsilon$-fixed point of a contraction map $f:[0,1]^k\mapsto[0,1]^k$ under the $\ell_\infty$-norm with query complexity $O (k\log (1/\epsilon ) )$.
In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems…
In this paper we obtain improved iteration complexities for solving $\ell_p$ regression. We provide methods which given any full-rank $\mathbf{A} \in \mathbb{R}^{n \times d}$ with $n \geq d$, $b \in \mathbb{R}^n$, and $p \geq 2$ solve…
We study an extension of the Arrival problem, called Recursive Arrival, inspired by Recursive State Machines, which allows for a family of switching graphs that can call each other in a recursive way. We study the computational complexity…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
In the classical longest palindromic substring (LPS) problem, we are given a string $S$ of length $n$, and the task is to output a longest palindromic substring in $S$. Gilbert, Hajiaghayi, Saleh, and Seddighin [SPAA 2023] showed how to…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…