Abstract:

We study the computational complexities of three problems on multi-agent scheduling on a single machine. Among the three problems, the computational complexities of the first two problems were still open and the last problem was shown to be unary NP-hard in the literature. We show in this paper that the first two problems are unary NP-hard. We also show that the unary NP-hardness proof for the last problem in the literature is invalid, and so, the exact complexity of the problem is still open.

Key words: Multi-agent scheduling ·, Competing agents ·, Non-disjoint agents ·, Unary NP-hard