man wncp (Fonctions bibliothèques) - critical path problem

NAME

wn_critical_path - critical path problem

SYNOPSIS

#include <wn/wnspmat.h>
#include <wn/wncp.h>

wn_critical_path(&code,&len,&result,length_mat,start_node,fin_node)
int code;
double len;
wn_sll result; /* list of edges */
wn_sparse_matrix length_mat;
int start_node,fin_node;

DESCRIPTION

This package solves the "critical path" problem easily and efficiently. length_mat is treated as a DIRECTED GRAPH; thus it must be square. The matrix entry length_mat[i][j] gives the length of the directed edge from node i to node j. Negative edge lengths are allowed. length_mat must be a DAG; it must contain no cycles or undirected edges. result is the list of edges in the critical path, ordered starting from start_node. len is set to the total length of the solution.

The critical path problem is the following optimization problem:

Choose the path in the graph length_mat from start_node to fin_node which is the longest possible path.

Difficult optimization problems from many fields can be put into this form, and thus solved efficiently with this package.

For an introduction to the critical path problem, consult [1].

RESOURCES

Solving a critical path problem requires

AVERAGE CASE:

time = e stack memory = 1 dynamic memory = n

WORST CASE:

time = e stack memory = n dynamic memory = n

where e is the number of matrix entries, and n is the number of nodes in the graph represented by length_mat. (n == len_i == len_j).

DIAGNOSTICS

code == WN_SUCCESS for successful solution. code == WN_INFEASIBLE if no path from start_node to fin_node exists, or if the graph contains cycles or undirected edges.

len_i != len_j causes a crash.

SEE ALSO

wnsp, wnlp, wnsplx

AUTHOR

Will Naylor

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