{"type":"ScholarlyArticle","title":"From Approximate to Optimal Solutions: A Case Study of Number Partitioning","authors":[{"name":"Richard E. Korf","slug":"richard-e-korf","given":"Richard E.","family":"Korf","affiliation":""}],"abstract":"Given a set of numbers, the two-way partitioning problem is to divide them into two subsets, so that the sum of the numbers in each subset are as nearly equal as possible. The problem is NP-complete, and is contained in many scheduling applications. Based on a polynomial-time heuristic due to Karmarkar and Karp, we present a new algorithm, called Complete Karmarkar Karp (CKK), that optimally solves the general number-partitioning problem. CKK significantly outperforms the best previously-known algorithms for this problem. By restricting the numbers to twelve significant digits, we can optimally solve two-way partitioning problems of arbitrary size in practice. CKK first returns the Karmarkar-Karp solution, then continues to find better solutions as time allows. Almost five orders of magnitude improvement in solution quality is obtained within a minute of running time. Rather than building a single solution one element at a time, CKK constructs subsolutions, and combines them in all possible ways. CKK is directly applicable to the 0/1 knapsack problem, since it can be reduced to number partitioning. This general approach may also be applicable to other NP-hard problems as well.","doi":null,"url":"https://ijcai.org/proceedings/1995/35","pdf":"https://ijcai.org/proceedings/1995/0035.pdf","markdown":"https://ijcai.org/proceedings/1995/35.md","bibtex":"https://ijcai.org/proceedings/1995/bibtex/35","volume":{"slug":"1995","title":"Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1995","url":"https://ijcai.org/proceedings/1995/","year":1995,"location":"Montréal, Québec, Canada","dates":"","editors":"Chris S. Mellish","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Automated Reasoning","track":"Automated Reasoning","number":35,"pages":{"first":266,"last":271},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}