An Approximation Algorithm for the Precedence Constrained Scheduling Problem with Hierarchical Communications

General scheduling non-approximability results in presence of hierarchical communications

“…See [2] • The problem P 1 : is the problem Monotone-one-in-three-3SAT. Let us first recall the definition of Monotoneone-in-three-3SAT problem.…”

“…In this paper, we adopt the hierarchical communication model [5] in which we assume that the communication delays are not homogeneous anymore; the processors are connected into clusters and the communications inside a same cluster are much faster than those between processors belonging to different ones.…”

Scheduling with Communication Delays

“…We use the algorithm 1 for the rounding algorithm by changing the value rounded: e ij < 0.25 instead e ij < 0.5 The solution given by Step 1 is not necessarily a feasible solution (take for instance the precedence graph of Figure 1.7), so we must transform it to a feasible one. Notice that the cases given in Figure 1 (Bampis et al, 2003). Proof See the proof of the Theorem 1.2.3.…”

“…These complexity results are given in Table 1.1. On positive side, the authors presented in (Bampis et al, 2000b) a 8/5-approximation algorithm for the problem ;p i = 1 which is based on an integer linear programming formulation. They relax the integrity constraints and they produce a feasible schedule by rounding.…”

“…More precisely, scheduling problems involving precedence constraints are among the most difficult problems in the area of machine scheduling and they are part of the most studied problems in the domain. In this chapter, we adopt the hierarchical communication model (Bampis et al, 2003) in which we assume that the communication delays are not homogeneous anymore; the processors are connected into clusters and the communications Open Access Database www.i-techonline.com Source: Multiprocessor Scheduling: Theory and Applications, Book edited by Eugene Levner, ISBN 978-3-902613-02-8, pp.436, December 2007, Itech Education and Publishing, Vienna, Austria inside a same cluster are much faster than those between processors belonging to different ones. This model incorporates the hierarchical nature of the communications using today's parallel computers, as shown by many PCs or workstations networks (NOWs) (Pfister, 1995;Anderson et al, 1995).…”