Related papers: Going for Speed: Sublinear Algorithms for Dense r-…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
We consider the problem of efficiently scheduling jobs with precedence constraints on a set of identical machines in the presence of a uniform communication delay. Such precedence-constrained jobs can be modeled as a directed acyclic graph,…
In the $k$-Edit Circular Pattern Matching ($k$-Edit CPM) problem, we are given a length-$n$ text $T$, a length-$m$ pattern $P$, and a positive integer threshold $k$, and we are to report all starting positions of the substrings of $T$ that…
We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…
We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…
The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an…
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…
We consider the approximate pattern matching problem under the edit distance. Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold $k$, the task is to find the starting positions of all substrings of $T$ that can be…
We study pseudo-polynomial time algorithms for the fundamental \emph{0-1 Knapsack} problem. Recent research interest has focused on its fine-grained complexity with respect to the number of items $n$ and the \emph{maximum item weight}…
This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$. We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++. FastDrSub offers an…
We consider the classical $k$-Center problem in undirected graphs. The problem is known to have a polynomial-time 2-approximation. There are even $(2+\varepsilon)$-approximations running in near-linear time. The conventional wisdom is that…
$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…
Distributed computing systems often need to consider the scheduling problem involving a collection of highly dependent data-processing tasks that must work in concert to achieve mission-critical objectives. This paper considers the…
We present an algorithm that given a linear program with $n$ variables, $m$ constraints, and constraint matrix $A$, computes an $\epsilon$-approximate solution in $\tilde{O}(\sqrt{rank(A)}\log(1/\epsilon))$ iterations with high probability.…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $\lambda$ on graphs with…
We study the problem of approximating edit distance in sublinear time. This is formalized as the $(k,k^c)$-Gap Edit Distance problem, where the input is a pair of strings $X,Y$ and parameters $k,c>1$, and the goal is to return YES if…
Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…