Related papers: Improved Dynamic Algorithms for Longest Increasing…
We present an $O(1)$-round fully-scalable deterministic massively parallel algorithm for computing the min-plus matrix multiplication of unit-Monge matrices. We use this to derive a $O(\log n)$-round fully-scalable massively parallel…
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…
We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than $2$. Specifically, we obtain a…
In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time…
We study the entropy $S$ of longest increasing subsequences (LIS), i.e., the logarithm of the number of distinct LIS. We consider two ensembles of sequences, namely random permutations of integers and sequences drawn i.i.d.\ from a limited…
In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal…
We study the fundamental problem of sampling independent events, called subset sampling. Specifically, consider a set of $n$ events $S=\{x_1, \ldots, x_n\}$, where each event $x_i$ has an associated probability $p(x_i)$. The subset sampling…
We present a Las Vegas algorithm for dynamically maintaining a minimum spanning forest of an $n$-node graph undergoing edge insertions and deletions. Our algorithm guarantees an $O(n^{o(1)})$ worst-case update time with high probability.…
The edit distance is a fundamental measure of sequence similarity, defined as the minimum number of character insertions, deletions, and substitutions needed to transform one string into the other. Given two strings of length at most $n$,…
Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…
Clustering is an important task with applications in many fields of computer science. We study the fully dynamic setting in which we want to maintain good clusters efficiently when input points (from a metric space) can be inserted and…
Given a pair of strings, the problems of computing their Longest Common Subsequence and Edit Distance have been extensively studied for decades. For exact algorithms, LCS and Edit Distance (with character insertions and deletions) are…
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable…
Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…
This study investigates whether reoptimization can help in solving the closest substring problem. We are dealing with the following reoptimization scenario. Suppose, we have an optimal l-length closest substring of a given set of sequences…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
The minimum set cover (MSC) problem admits two classic algorithms: a greedy $\ln n$-approximation and a primal-dual $f$-approximation, where $n$ is the universe size and $f$ is the maximum frequency of an element. Both algorithms are simple…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…