# A Theory and Algorithms for Combinatorial Reoptimization

@article{Schieber2017ATA,
title={A Theory and Algorithms for Combinatorial Reoptimization},
author={Baruch Schieber and Hadas Shachnai and Gal Tamir and Tami Tamir},
journal={Algorithmica},
year={2017},
volume={80},
pages={576-607}
}
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 framework for combinatorial… Expand
39 Citations

#### Tables and Topics from this paper

Analysis and Experimental Study of Heuristics for Job Scheduling Reoptimization Problems
• Computer Science
• 2018
It is proved that the reoptimization variants of both problems are NP-hard, already for very restricted classes. Expand
• Mathematics
• 2018
This paper introduces a natural "reoptimization" meta-problem, which should be particularly relevant in faulty or dynamic networks. Fix any $\Delta > 0, \epsilon > 0$. Given two "approximate"Expand
On Lagrangian relaxation for constrained maximization and reoptimization problems
• Computer Science, Mathematics
• Discret. Appl. Math.
• 2021
Using the technique, (re)approximation algorithms for natural (reoptimization) variants of classic subset selection problems, including real-time scheduling, the maximum generalized assignment problem (GAP) and maximum weight independent set are obtained. Expand
Optimization and Reoptimization in Scheduling Problems
This work gives a polynomial time algorithm that yields for fully-feasible instances a schedule whose makespan is better than twice the optimal, the best known ratio for general instances, and develops reapproximation algorithms that yield in both models the best possible approximation ratio of $(1+\epsilon)$, with respect to the minimum makespan. Expand
An exact (re)optimization framework for real-time traffic management
• 2020
In real-time traffic management, a new schedule for the vehicles must be computed whenever a deviation from the current plan is detected, or periodically after some time. If this time interval isExpand
Multistage Knapsack
• Computer Science, Mathematics
• MFCS
• 2019
A PTAS is proposed for the Multistage Knapsack problem and it is proved that there is no FPTAS for the problem even in the case where T=2, unless P=NP, and a pseudopolynomial time algorithm is given for the cases where the number of steps is bounded by a fixed constant. Expand
Incremental optimization of independent sets under the reconfiguration framework
• Mathematics
• 2020
Suppose that we are given an independent set $$I_0$$ of a graph G, and an integer $$l\ge 0$$ . Then, we are asked to find an independent set of G having the maximum size among independent setsExpand
Cost-Oblivious Reallocation for Scheduling and Planning
• Computer Science
• SPAA
• 2015
A reallocating scheduler for the problem of assigning jobs to p (identical) servers is given so as to minimize the sum of completion times to within a constant factor of optimal, with an amortized reallocation cost for a length-w job of O(f(w)log3logΔ), where Delta is the length of the longest job and f() is the reallocated-cost function. Expand
A Generalized Matching Reconfiguration Problem
• Computer Science, Mathematics
• ITCS
• 2021
This paper introduces a natural generalization of the MRP that depends on an integer parameter $\Delta \ge 1$ and devise an optimal transformation procedure for unweighted matching with $\Delta = 3$, and then extend it to weighted matchings to achieve asymptotically optimal guarantees. Expand
Fast re-optimization via structural diversity
• Computer Science
• GECCO
• 2019
A simple diversity mechanism is proposed that prevents structurally good solutions during the optimization being replaced by structurally worse solutions of equal or better fitness, thereby reducing the re-optimization time for LeadingOnes to O(γδn), where γ is the population size used by the diversity mechanism and δ ≤ γ the Hamming distance of the new optimum from the previous solution. Expand

#### References

SHOWING 1-10 OF 82 REFERENCES
A Theory and Algorithms for Combinatorial Reoptimization
• Mathematics, Computer Science
• LATIN
• 2012
A general model for combinatorial reoptimization is developed, encompassing classical objective functions as well as the goal of minimizing the transition cost from one solution to the other, and distinguishes here for the first time between classes of re Optimization problems, by their hardness status with respect to minimizing transition costs while guaranteeing a good approximation for the underlying optimization problem. Expand
A Computational Study of Cost Reoptimization for Min-Cost Flow Problems
• Computer Science
• INFORMS J. Comput.
• 2006
This paper compares the performances of four different efficient implementations of algorithms for MCF under cost reoptimization in the context of decomposition algorithms for the multicommodity min-cost flow (MMCF) problem, showing that for some classes of instances the relative performances of the codes doing from-scratch optimization do not accurately predict therelative performances when re Optimization is used. Expand
On the Hardness of Reoptimization
• Mathematics, Computer Science
• SOFSEM
• 2008
The answer to this question depends on the considered problem and the type of local modification and can be totally different: for instance, for some reoptimization variant of the metric TSP, the authors get a 1.4-approximation improving on the best known approximation ratio of 1.5 for the classical metric T SP. Expand
Complexity and Approximation in Reoptimization
• Mathematics
• 2008
In this survey the following model is considered. We assume that an instance I of a computationally hard optimization problem has been solved and that we know the optimum solution of such instance.Expand
Reoptimization of the Shortest Common Superstring Problem
The NP-hardness of reoptimization variants of the shortest common superstring problem (SCS) where the local modifications consist of adding or removing a single string is shown and some lower bounds on the approximation ratio are given. Expand
On the parameterized complexity of dynamic problems
• Mathematics, Computer Science
• Theor. Comput. Sci.
• 2015
A study of the dynamic versions of a number of problems including Vertex cover, Maximum Clique, Connected Vertex Cover and Connected Dominating Set, and introduces the reoptimization parameter, which bounds the difference between the cardinalities of initial and target solutions. Expand
New approaches to multi-objective optimization
• Computer Science, Mathematics
• Math. Program.
• 2014
A simple mechanism to transform multi-criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system is presented and can be applied to the above bipartite matching algorithm, hence obtaining a pure PTAS. Expand
Optimization with More than One Budget
• Mathematics, Computer Science
• ArXiv
• 2010
It is shown that shortest path, perfect matching, and spanning tree are inapproximable already with two budget constraints, and deterministic and randomized polynomial-time approximation schemes for a constant number k of budget constraints are presented. Expand
On the Approximability of TSP on Local Modifications of Optimally Solved Instances
Given an instance of TSP together with an optimal solution, we consider the scenario in which this instance is modified locally, where a local modification consists in the alteration of the weight ofExpand
Reallocation Problems in Scheduling
• Computer Science
• Algorithmica
• 2014
This paper provides an algorithm that maintains a valid schedule, as long as a schedule with sufficient slack exists, and reschedules only a total number of jobs for each job that is inserted or deleted from the system. Expand