On the Task Assignment Problem : Two New Efficient Heuristic Algorithms

2 INTRODUCTION In this paper, we consider the problem of assigning tasks to processors in a distributed system in order to minimize the sum of interprocessor communication and task processing costs. In this paper, we transform the initial problem of minimization of total communication and execution costs into a maximization one, where we try to determine and avoid large communication and execution penalties.

3 MODEL DESCRIPTION Let P = {Pj, j = 1, 2,..., n} be the set of processors of a distributed computing system. T = {Ti, i = 1, 2,..., m} the set of tasks to be allocated. G(V, E) be the intertask communication graph. Let eip represent the cost of executing task i on processor p. ci j the communication cost between tasks i and j. xip, i = 1 · · · m, p = 1 · · · n, a 0, 1 variable, equal to 1 if task i runs on processor p and 0 otherwise.

4 GRAPH TRANSFORMATION

5

6

7 (4).

8 GRAPH TRANSFORMATION

9 MATCHING BASED HEURISTIC

10 THE MAXIMUM EDGE ALGORITHM

11 EXAMPLE :

12 COMPARATIVE STUDY During instance generation, the following parameters were considered:

13 COMPARATIVE STUDY As a measure of solution quality, the relative distance from the best solution was calculated for each of the three algorithms. For algorithm A, the relative distance from the best solution is defined as:

14 COMPARATIVE STUDY

15 COMPARATIVE STUDY

16 COMPARATIVE STUDY

17 COMPARATIVE STUDY

18 COMPARATIVE STUDY