A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
Competitive algorithms for server problems
Journal of Algorithms
Improved bounds for harmonic-based bin packing algorithms
Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
Online bin packing with lookahead
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
On the online bin packing problem
Journal of the ACM (JACM)
The 3-server problem in the plane
Theoretical Computer Science
On the Competitive Ratio of the Work Function Algorithm for the k-Server Problem
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Fully Dynamic Algorithms for Bin Packing: Being (mostly) Myopic Helps
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Removable Online Knapsack Problems
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Randomized Competitive Analysis for Two-Server Problems
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Online Knapsack Problems with Limited Cuts
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Online removable knapsack with limited cuts
Theoretical Computer Science
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Online minimization knapsack problem
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Theoretical Computer Science
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In this paper we study the Revocable Online Knapsack Problem (ROKP) which is an extension of the Online Knapsack Problem [8]. We prove an optimal upper bound of 1/t for the competitive ratio of ROKP, where t is a real root of 4x3 + 5x2 – x – 4 = 0 (t ≈0.76850 and 1/t ≈1.3012). To prove this result, we made a full use of computer programs as follows: For the base algorithm that is designed in a conventional manner, we first construct an equivalent finite state diagram with about 300 states. Then for each state, we generate a finite set of inequalities such that the competitive ratio at that state is at most 1/t if the set of inequalities do not have a real solution. The latter can be checked by Mathematica. The number of inequalities generated was approximately 600 in total, and our computation time was 30 minutes using Athlon XP 2600+.