On-Line Variable Sized Covering

We consider one-dimensional and multi-dimensional vector covering with variable sized bins. In the one-dimensional case, we consider variable sized bin covering with bounded item sizes. For every finite set of bins B, and upper bound 1/m on the size of items for some integer m, we define a ratio r(B, m). We prove this is the best possible competitive ratio for the set of bins B and the parameter m, by giving both an algorithm with competitive ratio r(B, m), and an upper bound of r(B, m) on the competitive ratio of any on-line deterministic or randomized algorithm. The ratio satisfies r(B, m) ≥ m/(m + 1), and

• Type: Conference
• Year: 2001
• Where: COCOON
• Authors: Leah Epstein
• Keywords: COCOON 2001, Combinatorics, Competitive Ratio, Upper Bound, Variable Sized Bin