Related papers: Upper and Lower Bounds for Deterministic Approxima…
Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
In a second seminal paper on the application of semidefinite programming to graph partitioning problems, Goemans and Williamson showed how to formulate and round a complex semidefinite program to give what is to date still the best-known…
A k-plex in a graph is a vertex set where each vertex is non-adjacent to at most k vertices (including itself) in this set, and the Maximum k-plex Problem (MKP) is to find the largest k-plex in the graph. As a practical NP-hard problem, MKP…
For any $\varepsilon > 0$, we prove that $k$-Dimensional Matching is hard to approximate within a factor of $k/(12 + \varepsilon)$ for large $k$ unless $\textsf{NP} \subseteq \textsf{BPP}$. Listed in Karp's 21 $\textsf{NP}$-complete…
This paper introduces OPTIMUM-DERAM, a highly consistent, scalable, secure, and decentralized shared memory solution. Traditional distributed shared memory implementations offer multi-object support by multi-threading a single object memory…
We study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack.…
Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…
Maximum surjective constraint satisfaction problems (Max-Sur-CSPs) are computational problems where we are given a set of variables denoting values from a finite domain B and a set of constraints on the variables. A solution to such a…
We construct a family of functions suitable for establishing lower bounds on the oracle complexity of first-order minimization of smooth strongly-convex functions. Based on this construction, we derive new lower bounds on the complexity of…
We consider approximation algorithms for covering integer programs of the form min $\langle c, x \rangle $ over $x \in \mathbb{N}^n $ subject to $A x \geq b $ and $x \leq d$; where $A \in \mathbb{R}_{\geq 0}^{m \times n}$, $b \in…
We consider static, external memory indexes for exact and approximate versions of the $k$-nearest neighbor ($k$-NN) problem, and show new lower bounds under a standard indivisibility assumption: - Polynomial space indexing schemes for…
We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of $n$ additive bidders whose values for $m$ heterogeneous items are drawn…
Using physical layer network coding, compute-and-forward is a promising relaying scheme that effectively exploits the interference between users and thus achieves high rates. In this paper, we consider the problem of finding the optimal…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a $(3/2-c)$-approximation algorithm for some fixed $c>0$, improving upon the long-standing bound of…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…