Efficient Approximation Algorithms for Scheduling Problems with Uniform P-Batch Machines and Arbitrary Processing Set Restrictions

We consider scheduling problems of processing a given set of independent jobs on parallel p-batch machines subject to arbitrary processing set restrictions (PSR). Two types of p-batch machines are considered: equal-speed and uniform. For the corresponding P- and Q-problems, efficient (strongly polynomial) approximation algorithms with a priori and a posteriori absolute and relative accuracy bounds have been designed. The presented results are the first attempt of an approximate solution of a that general problem (with arbitrary PSR and individual batch capacities of machines) in a strongly polynomial time and with performance ratios strictly less than two. As an auxiliary result, we have developed a new (linear-time) rounding algorithm for a given fractional distribution of jobs by machines in a tree-like graph.