Finding shuffle words that represent optimal scheduling of shared memory access

Abstract

In the present paper, we introduce and study the problem of computing, for any given finite set of words, a shuffle word with a minimum so-called scope coincidence degree. The scope coincidence degree is the maximum number of different symbols that parenthesize any position in the shuffle word. This problem is motivated by an application of a new automaton model and can be regarded as the problem of scheduling shared memory accesses of some parallel processes in a way that minimizes the number of memory cells required. We investigate the complexity of this problem and show that it can be solved in polynomial time.

Keywords:

• string algorithms
• shuffle
• memory access scheduling

2010 AMS Subject Classifications:

• 68Q25
• 68Q42
• 90B35
• 90C27