Efficient approximation algorithm design using function approximation

2016 Fiscal Year Final Research Report

• Project/Area Number: 15K15945
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: Sojo University
• Principal Investigator: ANDO Ei 崇城大学, 情報学部, 助教 (20583511)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Keywords: #P-困難問題 / 高次元多面体体積 / 完全多項式時間近似スキーム / FPTAS / 近似アルゴリズム

Outline of Final Research Achievements

In this research topic, three approximation algorithms have been proposed for the hard problems in the problem class of #P-hard. The three proposed algorithms are all fully polynomial time approximation schemes (FPTASes). First algorithm computes the volume of the knapsack polytope with multiple constraints. Second algorithm computes the volume of the geometric dual of the knapsack polytope. Third algorithm computes the probability distribution function of the longest path length in DAGs with random edge lengths. Although there are distinct techniques in each algorithms, the algorithms share one technique, the staircase approximation of the convolution integrals. One result is published refereed journal Algorithmica. The other results are (going to be) presented in refereed international coferences WALCOM2017 and COCOON2017.

Free Research Field

理論計算機科学