Related papers: Dynamic Longest Increasing Subsequence and the Erd…

We study dynamic algorithms for the longest increasing subsequence (\textsf{LIS}) problem. A dynamic \textsf{LIS} algorithm maintains a sequence subject to operations of the following form arriving one by one: (i) insert an element, (ii)…

We revisit the problem of maintaining the longest increasing subsequence (LIS) of an array under (i) inserting an element, and (ii) deleting an element of an array. In a recent breakthrough, Mitzenmacher and Seddighin [STOC 2020] designed…

Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple $O(n\log n)$ algorithms are known for this problem. We develop a polylogarithmic time randomized…

In this note, we present a substantial improvement on the computational complexity of the Erd\"{o}s-Szekeres partitioning problem and review recent works on dynamic \textsf{LIS}.

Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array…

We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…

We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…

Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…

This paper studies parallel algorithms for the longest increasing subsequence (LIS) problem. Let $n$ be the input size and $k$ be the LIS length of the input. Sequentially, LIS is a simple problem that can be solved using dynamic…

In this work, we present a plethora of results for the range longest increasing subsequence problem (Range-LIS) and its variants. The input to RLIS is a sequence $S$ of $n$ real numbers and a collection $Q$ of $m$ query ranges, and for each…

Estimating the length of the longest increasing subsequence (LIS) in an array is a problem of fundamental importance. Despite the significance of the LIS estimation problem and the amount of attention it has received, there are important…

We study the fully dynamic maximum matching problem. In this problem, the goal is to efficiently maintain an approximate maximum matching of a graph that is subject to edge insertions and deletions. Our focus is on algorithms that maintain…

In this note, we consider the complexity of maintaining the longest increasing subsequence (LIS) of an array under (i) inserting an element, and (ii) deleting an element of an array. We show that no algorithm can support queries and updates…

The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common…

In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…

The Longest Common Subsequence (LCS) of two strings is a fundamental string similarity measure with a classical dynamic programming solution taking quadratic time. Despite significant efforts, little progress was made in improving the…

Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…

In this paper, we construct a data structure to efficiently compute the longest increasing subsequence of a sequence subject to dynamic updates. Our data structure supports a query for the longest increasing subsequence in $O(r+\log n)$…

There are efficient dynamic programming solutions to the computation of the Edit Distance from $S\in[1..\sigma]^n$ to $T\in[1..\sigma]^m$, for many natural subsets of edit operations, typically in time within $O(nm)$ in the worst-case over…

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…