Related papers: A New Algorithm for Finding Closest Pair of Vector…
We present an efficient algorithm for the min-max correlation clustering problem. The input is a complete graph where edges are labeled as either positive $(+)$ or negative $(-)$, and the objective is to find a clustering that minimizes the…
The $k$-mismatch problem consists in computing the Hamming distance between a pattern $P$ of length $m$ and every length-$m$ substring of a text $T$ of length $n$, if this distance is no more than $k$. In many real-world applications, any…
Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…
The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the…
This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $\mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $\mathsf{ApproxMC}$ is…
We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $\Omega(n \log n)$ time.…
There has been significant success in designing highly efficient algorithms for distance and shortest-path queries in recent years; many of the state-of-the-art algorithms use the hub labeling framework. In this paper, we study the…
Filtered Approximate Nearest Neighbor (ANN) search retrieves the closest vectors for a query vector from a dataset. It enforces that a specified set of discrete labels $S$ for the query must be included in the labels of each retrieved…
We show how to compute any symmetric Boolean function on $n$ variables over any field (as well as the integers) with a probabilistic polynomial of degree $O(\sqrt{n \log(1/\epsilon)})$ and error at most $\epsilon$. The degree dependence on…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
We are given a set of points $p_1,\ldots , p_n$ and a symmetric distance matrix $(d_{ij})$ giving the distance between $p_i$ and $p_j$. We wish to construct a tour that minimizes $\sum_{i=1}^n \ell(i)$, where $\ell(i)$ is the {\em latency}…
$\newcommand{\popt}{{\mathcal{p}}} \newcommand{\Re}{\mathbb{R}}\newcommand{\N}{{\mathcal{N}}} \newcommand{\BX}{\mathcal{B}} \newcommand{\bb}{\mathsf{b}} \newcommand{\eps}{\varepsilon} \newcommand{\polylog}{\mathrm{polylog}} $ Let…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…
This work considers the problem of quickest detection of signals in a coupled system of N sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled a general Ito…
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on $n$ vertices whose edge weights are chosen independently and uniformly at random from $[0,1]$ is $O(n^2)$, in expectation and with high…
Given $x \in (\mathbb{R}_{\geq 0})^{\binom{[n]}{2}}$ recording pairwise distances, the METRIC VIOLATION DISTANCE (MVD) problem asks to compute the $\ell_0$ distance between $x$ and the metric cone; i.e., modify the minimum number of entries…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…