Browse > Article

Sub-Exponential Algorithm for 0/1 Knapsack  

Rhee, Chung Sei (충북대학교 소프트웨어학과)
Publication Information
Convergence Security Journal / v.14, no.7, 2014 , pp. 59-64 More about this Journal
Abstract
We investigate $p(n){\cdot}2^{O(\sqrt{n})}$ algorithm for 0/1 knapsack problem where x is the total bit length of a list of sizes of n objects. The algorithm is adaptable of method that achieves a similar complexity for the partition and Subset Sum problem. The method can be applied to other optimization or decision problem based on a list of numerics sizes or weights. 0/1 knapsack problem can be used to solve NP-Complete Problems with pseudo-polynomial time algorithm. We try to apply this technique to bio-informatics problem which has pseudo-polynomial time complexity.
Keywords
knapsack; NP; sub-exponential; algorithm; bio-informatics; Partition; Pseudo-Polynomial;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Alehnovich, A. Borodin, J. Buresh-Oppenheim, "Toward a Model for Backtracking and Dynamic Programming,", Proc of the 20th Annual IEEE Conferencen Computational Complexity, pp. 308-322, 2005.
2 M Garey and D. Johnson, Computers and Intractability : A Guide to the Theory of NP Completenes, Freeman Press, San Fransisco, CA, 1979.
3 R. Impagliazzo, R. Paturi and F. Zane, " Which Problems have Strongly Exponential Complexity?.", Journal of Computer and System Sciences 63, pp. 512-530, Elsevier Science 2001.   DOI
4 S. Martello and P. Toth, "A mixture of Dynamic programming and branch-and-bound for subset sum problem,", Management Science 30(6), pp. 765-771, 1984.   DOI
5 R. Stearns and H. Hunt, "Power indices and Easier Hard Problems", Mathematical System Thoery 23, pp. 209-225, 1990.   DOI
6 G. J. Woeginger, "Exact Algorithms for NP-Hard Problems: A Survey,", Lecture Notes in Computer Science 2570, pp. 185-207, Spring-Verlaugh, Berlin, 2003.