
Improved Dynamic Algorithms for Longest Increasing Subsequence
We study dynamic algorithms for the longest increasing subsequence (LIS)...
read it

Fully Dynamic Approximation of LIS in Polylogarithmic Time
We revisit the problem of maintaining the longest increasing subsequence...
read it

Dynamic Set Cover: Improved Amortized and WorstCase Update Time
In the dynamic minimum set cover problem, a challenge is to minimize the...
read it

A Partitioning Algorithm for Detecting Eventuality Coincidence in Temporal Double recurrence
A logical theory of regular double or multiple recurrence of eventualiti...
read it

Partitioning Vectors into Quadruples: WorstCase Analysis of a MatchingBased Algorithm
Consider a problem where 4k given vectors need to be partitioned into k ...
read it

A (2+ε)Approximation Algorithm for Maximum Independent Set of Rectangles
We study the Maximum Independent Set of Rectangles (MISR) problem, where...
read it

Rounding Dynamic Matchings Against an Adaptive Adversary
We present a new dynamic matching sparsification scheme. From this schem...
read it
Dynamic Longest Increasing Subsequence and the ErdösSzekeres Partitioning Problem
In this paper, we provide new approximation algorithms for dynamic variations of the longest increasing subsequence (LIS) problem, and the complementary distance to monotonicity (DTM) problem. In this setting, operations of the following form arrive sequentially: (i) add an element, (ii) remove an element, or (iii) substitute an element for another. At every point in time, the algorithm has an approximation to the longest increasing subsequence (or distance to monotonicity). We present a (1+ϵ)approximation algorithm for DTM with polylogarithmic worstcase update time and a constant factor approximation algorithm for LIS with worstcase update time Õ(n^ϵ) for any constant ϵ > 0. the time the operation arrives. Our dynamic algorithm for LIS leads to an almost optimal algorithm for the ErdösSzekeres partitioning problem. ErdösSzekeres partitioning problem was introduced by Erdös and Szekeres in 1935 and was known to be solvable in time O(n^1.5log n). Subsequent work improve the runtime to O(n^1.5) only in 1998. Our dynamic LIS algorithm leads to a solution for ErdösSzekeres partitioning problem with runtime Õ_ϵ(n^1+ϵ) for any constant ϵ > 0.
READ FULL TEXT
Comments
There are no comments yet.