Shortest Superstring Problem

Given a list of strings where no string is substring of another, find a shortest string that contains each string in given list as a substring.  

Job Sequencing Problem with Deadlines

Given a set of tasks with deadlines and total profit earned on completion of a task, find maximum profit earned by executing the tasks within the specified deadlines. Assume any task will take one unit of time to execute and any task can’t execute beyond its deadline. Also, only one task can be executed at …

Greedy coloring of graph

Greedy coloring of graph

The graph coloring (also called as vertex coloring) is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color. In this post we will discuss a greedy algorithm for graph coloring and try to minimize the number of colors used.

Activity Selection Problem

In Activity Selection Problem, we’re given a set of activities and the starting & finishing time of each activity, we need to find the maximum number of activities that can be performed by a single person assuming that a person can only work on a single activity at a time.  

All-Pairs Shortest Paths – Floyd Warshall Algorithm

Given a set of vertices V in a weighted graph where its edge weights w(u, v) can be negative, find the shortest-path weights d(s, v) from every source s for all vertices v present in the graph. If the graph contains negative-weight cycle, report it.

Single-Source Shortest Paths – Bellman Ford Algorithm

Given a source vertex s from set of vertices V in a weighted graph where its edge weights w(u, v) can be negative, find the shortest-path weights d(s, v) from given source s for all vertices v present in the graph. If the graph contains negative-weight cycle, report it.

Single-Source Shortest Paths – Dijkstra’s Algorithm

Given a source vertex s from set of vertices V in a weighted graph where all its edge weights w(u, v) are non-negative, find the shortest-path weights d(s, v) from given source s for all vertices v present in the graph.