Related papers: Approximating Long Cycle Above Dirac's Guarantee
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
Many practical problems need the output of a machine learning model to satisfy a set of constraints, $K$. Nevertheless, there is no known guarantee that classical neural network architectures can exactly encode constraints while…
Universal Approximation Theorems establish the density of various classes of neural network function approximators in $C(K, \mathbb{R}^m)$, where $K \subset \mathbb{R}^n$ is compact. In this paper, we aim to extend these guarantees by…
Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
We give a polynomial-time algorithm for detecting very long cycles in dense regular graphs. Specifically, we show that, given $\alpha \in (0,1)$, there exists a $c=c(\alpha)$ such that the following holds: there is a polynomial-time…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
The Lasserre Hierarchy is a set of semidefinite programs which yield increasingly tight bounds on optimal solutions to many NP-hard optimization problems. The hierarchy is parameterized by levels, with a higher level corresponding to a more…
For a given graph $G$ of minimum degree at least $k$, let $G_p$ denote the random spanning subgraph of $G$ obtained by retaining each edge independently with probability $p=p(k)$. We prove that if $p \ge \frac{\log k + \log \log k +…
We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…
The Cycle Packing problem asks whether a given undirected graph $G=(V,E)$ contains $k$ vertex-disjoint cycles. Since the publication of the classic Erd\H{o}s-P\'osa theorem in 1965, this problem received significant scientific attention in…
We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…
In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms…
We give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…
We give nearly-tight upper and lower bounds for the improving multi-armed bandits problem. An instance of this problem has $k$ arms, each of whose reward function is a concave and increasing function of the number of times that arm has been…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…
Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online…
We refine a property of $2$-connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that each $2$-connected $n$-vertex graph with minimum degree at…