Uther Le 31/03/2008 à 13:35 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
on peut joindre n’importe quelle paire de point de l’ensemble en restant dans cet ensemble
Je ne suis pas développeur Java : je suis artiste Java.
Ce que l’on conçoit bien s’énonce clairement, / Et le code pour l’écrire arrive aisément.
Hâtez-vous lentement ; toujours, avec méthode, / Vingt fois dans l’IDE travaillez votre code.
La perfection est atteinte, non pas lorsqu’il n’y a plus rien à ajouter, mais lorsqu’il n’y a plus rien à retirer.
You don't use science to show that you're right, you use science to become right.
The algorithm works by increasing the number of zeros in the matrix and searching for a set of starred zeros, one in every row and column. Zeros are primed, starred, or neither during the algorithm. If there are insufficient zeros a quick addition and subtraction process adds more. If there are not enough starred zeros, the primed zeros are starred and the starred zeros primed. Primed zeros are zeros in a column without any more zeros, which, because they are in the same row as another zero were not starred.
The procedure of obtaining the prime zeros can be implemented in a flow network, and automated by means of the Ford-Fulkerson algorithm. The n×m matrix is transformed in a G = (U,V) bipartite graph, with I/O capacity equal to 1. Each arc joining the nodes of the flow network represents a zero in the cost matrix. After the maximum flow is obtained, the affected arcs represent the prime zeros. The minimum cut obtained by Ford-Fulkerson automates the process of marking the independent zeros. Each node that gets "cut" on the max-flow graph represents a marked column or line on the cost matrix. In the Hungarian method, assignment can be easily found on the cost matrix, yet the expansion into a max-flow sub-problem is a useful method in more complex scenarios.
<<< Kernel Extremis©®™ >>> et Inventeur de la différence administratif/judiciaire ! (©Yoshi Noir)
<Vertyos> un poil plus mais elle suce bien quand même la mienne ^^
<Sabrina`> tinkiete flan c juste qu'ils sont jaloux que je te trouve aussi appétissant
An arbitrary assignment is shown above in which worker a is assigned job q, worker b is assigned job s and so on. The total cost of this assignment is 23. Can you find a lower cost assignment? Can you find the minimal cost assignment? Remember that each assignment must be unique in its row and column.
A brute-force algorithm for solving the assignment problem involves generating all independent sets of the matrix C, computing the total costs of each assignment and a search of all assignment to find a minimal-sum independent set. The complexity of this method is driven by the number of independent assignments possible in an nxn matrix. There are n choices for the first assignment, n-1 choices for the second assignment and so on, giving n! possible assignment sets. Therefore, this approach has, at least, an exponential runtime complexity.
<<< Kernel Extremis©®™ >>> et Inventeur de la différence administratif/judiciaire ! (©Yoshi Noir)
<Vertyos> un poil plus mais elle suce bien quand même la mienne ^^
<Sabrina`> tinkiete flan c juste qu'ils sont jaloux que je te trouve aussi appétissant
Step 0: Create an nxm matrix called the cost matrix in which each element represents the cost of assigning one of n workers to one of m jobs. Rotate the matrix so that there are at least as many rows as columns and let k=min(n,m).
Step 1: For each row of the matrix, find the smallest element and subtract it from every element in its row. Go to Step 2.
Step 2: Find a zero (Z) in the resulting matrix. If there is no starred zero in its row or column, star Z. Repeat for each element in the matrix. Go to Step 3.
Step 3: Cover each column containing a starred zero. If K columns are covered, the starred zeros describe a complete set of unique assignments. In this case, Go to DONE, otherwise, Go to Step 4.
Step 4: Find a noncovered zero and prime it. If there is no starred zero in the row containing this primed zero, Go to Step 5. Otherwise, cover this row and uncover the column containing the starred zero. Continue in this manner until there are no uncovered zeros left. Save the smallest uncovered value and Go to Step 6.
Step 5: Construct a series of alternating primed and starred zeros as follows. Let Z0 represent the uncovered primed zero found in Step 4. Let Z1 denote the starred zero in the column of Z0 (if any). Let Z2 denote the primed zero in the row of Z1 (there will always be one). Continue until the series terminates at a primed zero that has no starred zero in its column. Unstar each starred zero of the series, star each primed zero of the series, erase all primes and uncover every line in the matrix. Return to Step 3.
Step 6: Add the value found in Step 4 to every element of each covered row, and subtract it from every element of each uncovered column. Return to Step 4 without altering any stars, primes, or covered lines.
DONE: Assignment pairs are indicated by the positions of the starred zeros in the cost matrix. If C(i,j) is a starred zero, then the element associated with row i is assigned to the element associated with column j.
<<< Kernel Extremis©®™ >>> et Inventeur de la différence administratif/judiciaire ! (©Yoshi Noir)
<Vertyos> un poil plus mais elle suce bien quand même la mienne ^^
<Sabrina`> tinkiete flan c juste qu'ils sont jaloux que je te trouve aussi appétissant
Linux Developer Gets Laid
Je ne suis pas développeur Java : je suis artiste Java.
Ce que l’on conçoit bien s’énonce clairement, / Et le code pour l’écrire arrive aisément.
Hâtez-vous lentement ; toujours, avec méthode, / Vingt fois dans l’IDE travaillez votre code.
La perfection est atteinte, non pas lorsqu’il n’y a plus rien à ajouter, mais lorsqu’il n’y a plus rien à retirer.
You don't use science to show that you're right, you use science to become right.
Trying to get up that great big hill of hope
For a destination
Je ne suis pas développeur Java : je suis artiste Java.
Ce que l’on conçoit bien s’énonce clairement, / Et le code pour l’écrire arrive aisément.
Hâtez-vous lentement ; toujours, avec méthode, / Vingt fois dans l’IDE travaillez votre code.
La perfection est atteinte, non pas lorsqu’il n’y a plus rien à ajouter, mais lorsqu’il n’y a plus rien à retirer.
You don't use science to show that you're right, you use science to become right.
protected static final Tag VERSION = new Tag( "Version" ) ;
Je ne suis pas développeur Java : je suis artiste Java.
Ce que l’on conçoit bien s’énonce clairement, / Et le code pour l’écrire arrive aisément.
Hâtez-vous lentement ; toujours, avec méthode, / Vingt fois dans l’IDE travaillez votre code.
La perfection est atteinte, non pas lorsqu’il n’y a plus rien à ajouter, mais lorsqu’il n’y a plus rien à retirer.
You don't use science to show that you're right, you use science to become right.
