Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Better approximations for max TSP
Information Processing Letters
Note: An improved randomized approximation algorithm for maximum triangle packing
Discrete Applied Mathematics
A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Deterministic 7/8-approximation for the metric maximum TSP
Theoretical Computer Science
An approximation algorithm for maximum triangle packing
Discrete Applied Mathematics
Improved deterministic approximation algorithms for Max TSP
Information Processing Letters
Approximation hardness for small occurrence instances of NP-hard problems
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
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We give derandomizations of known randomized approximation algorithms for the maximum traveling salesman problem and the maximum triangle packing problem: we show how to define pessimistic estimators for certain probabilities, based on the analysis of the randomized algorithms, and show that we can multiply the estimators to obtain pessimistic estimators for the expected weight of the solution. The method of pessimistic estimators (Raghavan (1988) [14]) then immediately implies that the randomized algorithms can be derandomized. For the maximum triangle packing problem, this gives deterministic algorithms with better approximation guarantees than what was previously known. The key idea in our analysis is the specification of conditions on pessimistic estimators of two expectations E[Y] and E[Z], under which the product of the pessimistic estimators is a pessimistic estimator of E[YZ], where Y and Z are two random variables. This approach can be useful when derandomizing algorithms for which one needs to bound the probability of some event that can be expressed as an intersection of multiple events; using our method, one can define pessimistic estimators for the probabilities of the individual events, and then multiply them to obtain a pessimistic estimator for the probability of the intersection of the events.