GraphRanker

Individual project for Algorithms and Principles of Computer Science course at Politecnico di Milano

Grade: 30/30 Cum Laude

Project Assignment

The assignment consists of writing a C program that manages a ranking of weighted directed graphs. Given two blank-separated integers d and k which are the number of nodes in a graph and the ranking size, respectively, the program has to print the top k graphs it has seen since the beginning of the execution, based on ranking metrics defined below. Every graph is labeled with a number representing the amount of graphs that have been read before it, starting from 0.

The program accepts two commands:

• AggiungiGrafo [adjacency matrix]: add a graph to those considered to draw up the ranking

E.g.:

AggiungiGrafo
3,7,42
0,7,2
7,4,3

• TopK: print the labels of the top k graphs received until that point, on a single line, blank-separated, in any order

Graphs have to be ranked based on the following metrics:

• Sum of all minimum-length paths from node 0 to all nodes reachable from 0 shall be minimum
• Paths to nodes not reachable from node 0 are considered of zero length
• If two graphs reach the same metric value, the oldest one stays

Execution sample

Input:
3,2                       3-nodes graphs, print the 2 best graphs
AggiungiGrafo             First graph added (index 0, paths sum = 7)
0,4,3
0,2,0
2,0,0
AggiungiGrafo             Second graph added (index 1, paths sum = 5)
0,0,2
7,0,4
0,1,0
AggiungiGrafo             Third graph added (index 2, paths sum = 7)
3,1,8
0,0,5
0,9,0
TopK

Output:
0 1 Or 1 0

Code Description

The ranking is implemented as a Max-Heap, which is stored as an array starting from index 1 (0th position is ignored). Given i the index of the current node, its left and right children are respectively at indexes 2*i and 2*i+1, while its parent is at index i/2. These are then compiled as shift left/right cpu instructions which result in very quick indexes calculations.

Every graph is read as a matrix and gets assigned a score based on the above metrics, which is then used to determine its position in the ranking. The score is calculated using the Dijkstra algorithm, which has a time complexity of Θ(V² + E) and a space complexity of Θ(V + E), where V is the number of nodes and E represent the number of links.