Parallel Algorithms for Two Processors Precedence Constraint Scheduling

Years and Authors of Summarized Original Work

• 2003; Jung, Serna, Spirakis

Problem Definition

In the general form of multiprocessor precedence scheduling problems a set of n tasks to be executed on m processors is given. Each task requires exactly one unit of execution time and can run on any processor. A directed acyclic graph specifies the precedence constraints where an edge from task x to task y means task x must be completed before task y begins. A solution to the problem is a schedule of shortest length indicating when each task is started. The work of Jung, Serna, and Spirakis provides a parallel algorithm (on a PRAM machine) that solves the above problem for the particular case that ${ m=2 }$, that is where there are two parallel processors.

The two processor precedence constraint scheduling problem is defined by a directed acyclic graph (dag) ${ G=(V,E) }$. The vertices of the graph represent unit time tasks, and the edges specify precedence constraints among the...