Experimental analysis of dynamic minimum spanning tree algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
When does a dynamic programming formulation guarantee the existence of an FPTAS?
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Dynamic Graph Algorithms with Applications
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Lagrangean heuristics combined with reoptimization for the 0-1 bidimensional knapsack problem
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
A Computational Study of Cost Reoptimization for Min-Cost Flow Problems
INFORMS Journal on Computing
A New Approach for Tree Alignment Based on Local Re-Optimization
BMEI '08 Proceedings of the 2008 International Conference on BioMedical Engineering and Informatics - Volume 01
Reoptimization of the Shortest Common Superstring Problem
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Reoptimization of minimum and maximum traveling salesman's tours
Journal of Discrete Algorithms
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Reoptimizing the 0-1 knapsack problem
Discrete Applied Mathematics
A General Approach for Incremental Approximation and Hierarchical Clustering
SIAM Journal on Computing
Minimal cost reconfiguration of data placement in storage area network
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
A new algorithm for reoptimizing shortest paths when the arc costs change
Operations Research Letters
Parameterized Complexity
Reoptimization of the minimum total flow-time scheduling problem
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Reallocation problems in scheduling
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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Many real-life applications involve systems that change dynamically over time. Thus, throughout the continuous operation of such a system, it is required to compute solutions for new problem instances, derived from previous instances. Since the transition from one solution to another incurs some cost, a natural goal is to have the solution for the new instance close to the original one (under a certain distance measure). In this paper we develop a general model for combinatorial reoptimization, encompassing classical objective functions as well as the goal of minimizing the transition cost from one solution to the other. Formally, we say that A is an (r, ρ)-reapproximation algorithm if it achieves a ρ-approximation for the optimization problem, while paying a transition cost that is at most r times the minimum required for solving the problem optimally. When ρ=1 we get an (r,1)-reoptimization algorithm. Using our model we derive reoptimization and reapproximation algorithms for several important classes of optimization problems. This includes fully polynomial time reapproximation schemes for DP-benevolent problems, a class introduced by Woeginger (Proc. Tenth ACM-SIAM Symposium on Discrete Algorithms, 1999), reapproximation algorithms for metric Facility Location problems, and (1,1)-reoptimization algorithm for polynomially solvable subset-selection problems. Thus, we distinguish here for the first time between classes of reoptimization problems, by their hardness status with respect to minimizing transition costs while guaranteeing a good approximation for the underlying optimization problem.