A Partitioning Algorithm for Detecting Eventuality Coincidence in Temporal Double recurrence

04/29/2017
by   B. O. Akinkunmi, et al.
0

A logical theory of regular double or multiple recurrence of eventualities, which are regular patterns of occurrences that are repeated, in time, has been developed within the context of temporal reasoning that enabled reasoning about the problem of coincidence. i.e. if two complex eventualities, or eventuality sequences consisting respectively of component eventualities x0, x1,....,xr and y0, y1, ..,ys both recur over an interval k and all eventualities are of fixed durations, is there a subinterval of k over which the occurrence xp and yq for p between 1 and r and q between 1 and s coincide. We present the ideas behind a new algorithm for detecting the coincidence of eventualities xp and yq within a cycle of the double recurrence of x and y. The algorithm is based on the novel concept of gcd partitions that requires the partitioning of each of the incidences of both x and y into eventuality sequences each of which components have a duration that is equal to the greatest common divisor of the durations of x and y. The worst case running time of the partitioning algorithm is linear in the maximum of the duration of x and that of y, while the worst case running time of an algorithm exploring a complete cycle is quadratic in the durations of x and y. Hence the partitioning algorithm works faster than the cyclical exploration in the worst case.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/29/2017

The Problem of Coincidence in A Theory of Temporal Multiple Recurrence

Logical theories have been developed which have allowed temporal reasoni...
research
01/31/2018

Constant Factor Time Optimal Multi-Robot Routing on High-Dimensional Grids in Mostly Sub-Quadratic Time

Let G = (V, E) be an m_1 ×...× m_k grid. Assuming that each v ∈ V is occ...
research
09/19/2023

Worst-Case and Smoothed Analysis of Hartigan's Method for k-Means Clustering

We analyze the running time of Hartigan's method, an old algorithm for t...
research
01/18/2021

Dynamic Longest Increasing Subsequence and the Erdös-Szekeres Partitioning Problem

In this paper, we provide new approximation algorithms for dynamic varia...
research
01/17/2023

Subset Sum in Time 2^n/2 / poly(n)

A major goal in the area of exact exponential algorithms is to give an a...
research
11/09/2022

Fully-dynamic-to-incremental reductions with known deletion order (e.g. sliding window)

Dynamic algorithms come in three main flavors: 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡𝑎𝑙 (insertions-o...
research
11/30/2019

Exact Polynomial Time Algorithm for the Response Time Analysis of Harmonic Tasks with Constrained Release Jitter

In some important application areas of hard real-time systems, preemptiv...

Please sign up or login with your details

Forgot password? Click here to reset