Algorithm NextFit for the Bin Packing Problem

Summary . The bin packing problem is a fundamental and important optimization in theoretical computer science [4], [6]. An instance sequence of items, each being positive size at most one. task to place all the items into bins so that total one number contain least item minimum. Approximation algorithms have been intensively studied. Algorithm NextFit would be simplest algorithm repeatedly does following: If first unprocessed can placed, terms size, additionally which has placed an last time, bin; otherwise empty bin. Johnson [5] proved resulting by less than twice fewest are needed items. In this article, we formalize Mizar [1], [2] as follows: real numbers find function maps indices integers such sum subsequence for inverse images image We then NextFit, its feasibility, approximation guarantee, tightness guarantee.