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algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O((

algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O((

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O((n+m)*T).

However, we have a problem: at every time step, a subset of vertices of this graph undergo maintenance and if the robot is on one of these vertices at this time step, it will be destroyed (!). Luckily, we are given the schedule of the maintenance for the next T time steps in an array M[1: T], where each M[i] is a linked-list of the vertices that undergo maintenance at time step i. Design an algorithm that finds a route for the robot to go from s to t in at most T seconds so that at no time i, the robot is on one of the maintained vertices, or output that this is not possible. The runtime of your algorithm should ideally be O((n + m)-T) but you will receive partial credit for worse runtime also.
Transcribed Image Text:However, we have a problem: at every time step, a subset of vertices of this graph undergo maintenance and if the robot is on one of these vertices at this time step, it will be destroyed (!). Luckily, we are given the schedule of the maintenance for the next T time steps in an array M[1: T], where each M[i] is a linked-list of the vertices that undergo maintenance at time step i. Design an algorithm that finds a route for the robot to go from s to t in at most T seconds so that at no time i, the robot is on one of the maintained vertices, or output that this is not possible. The runtime of your algorithm should ideally be O((n + m)-T) but you will receive partial credit for worse runtime also.
We are given an undirected connected graph G = (V, E) and vertices s and t. Initially, there is a robot at positions and we want to move this robot to position t by moving it along the edges of the graph; at any time step, we can move the robot to one of the neighboring vertices and the robot will reach that vertex in the next time step.
Transcribed Image Text:We are given an undirected connected graph G = (V, E) and vertices s and t. Initially, there is a robot at positions and we want to move this robot to position t by moving it along the edges of the graph; at any time step, we can move the robot to one of the neighboring vertices and the robot will reach that vertex in the next time step.
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