Capacitated Max-Batching with interval graph compatibilities

We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the cost of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving an open question from [7, 4, 5], we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.

• Type: Journal
• Year: 2016
• Where: TCS
• Authors: Tim Nonner
• Keywords: TCS 2016, Theoretical Computer Science