We propose a general approach for nding minmax regret solutions for a class of combinatorial optimization problems with an objective function of minimax type and uncertain objective function coe cients. The approach is based on reducing a problem with uncertainty to a number of problems without uncertainty. The method is illustrated on bottleneck combinatorial optimization problems, minimax mul...

We develop a model of multi-candidate electoral competition in a multi-dimensional policy space with strategic voters. We show that when the distribution of voter ideal points is log-concave, there exist pure-strategy subgame perfect equilibria in weakly undominated strategies in which platforms are located in the minmax set. Analytical and numerical results suggest that the size of the minmax ...

Given an acyclic directed graph and two distinct nodes s and t, we consider the problem of finding k disjoint paths from s to t satisfying some objective. We consider four objectives, MinMax, Balanced, MinSum-MinMin, and MinSum-MinMax. We use the algorithm by Perl-Shiloach and labelling and scaling techniques to devise an FPTAS for the first three objectives. For the forth one, we propose a gen...

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The two-watchman route problem is that of computing a pair of closed tours in an environment so that the two tours together see the whole environment and some length measure on the two tours is minimized. Two standard measures are: the minmax measure, where we want the tours where the longest of them has minimal length, and the minsum measure, where we want the tours for which the sum of their ...

HUGO is the content-based adaptive steganography method for spatial images which can approximately preserve the joint statistic of differences between up to four neighboring pixels in four different directions. But the steganalysis method based on the higher order local model can fail HUGO. In view of the above problem, an improved steganography is proposed. Firstly, by analyzing the higher ord...

Mining operations can produce highly localized, low intensity earthquakes that are referred to as microseismic events. Monitoring of microseismic events is useful in predicting and comprehending hazards, and in evaluating the overall performance of a mine design. A robust localization algorithm is used to estimate the source position of the microseismic event by selecting the hypothesized sourc...

Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90’s and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust d...

Recurrence relations with minimization and maximization, called minmax recurrence relations are commonly encountered in the analysis of algorithms. In this paper we present the solution of one such challenging recurrence relation. We characterize the optimal partition sizes as well as derive the order of complexity of the overall recurrence relation. It is proved that ad hoc equal partitioning ...

Adaptive array processing algorithms have achieved widespread use because they are very effective at rejecting unwanted signals (i.e., controlling sidelobe levels) and in general have very good resolution (i.e., have narrow mainlobes). However, many adaptive high-resolution array processing algorithms suffer a significant degradation in performance in the presence of environmental mismatch. Thi...