We examine powers of Hamiltonian paths and cycles as well as Hamiltonian (power) completion problems in several highly structured graph classes. For threshold graphs we give efficient algorithms as well as sufficient and minimax toughness like conditions. For arborescent comparability graphs we have similar results but also show that for one type of completion problem an ‘obvious’ minimax condi...

Game tree search algorithms such as minimax have been used with enormous success in turn-based adversarial games such as Chess or Checkers. However, such algorithms cannot be directly applied to real-time strategy (RTS) games because a number of reasons. For example, minimax assumes a turn-taking game mechanics, not present in RTS games. In this paper we present RTMM, a real-time variant of the...

This paper presents a least-pth approach for the design of complex-coefficient FIR digital filters with low group delay in the minimax sense. Features of the proposed approach include: it does not need to adapt the weighting function involved and no constrains are imposed during the course of optimization. More important, the algorithm enjoys global convergence to the minimax design regardless ...

We consider ill-conditioned mixture-models with varying mixing-weights. We study the classical homogeneity testing problem in the minimax setup and try to push the model to its limits, that is to say to let the mixture model to be really ill-conditioned. We highlight the strong connection between the mixing-weights and the expected rate of testing.This link is characterized by the behavior of t...

Many decision models can be formulated as continuous minimax problems. The minimax framework injects robustness into the model. It is a tool that one can use to perform worst–case analysis, and it can provide considerable insight into the decision process. It is frequently used alongside other methods such as expected value optimization in order to identify extreme scenarios and strategies that...

Abstract Recently, many researchers pay their attention to portfolio problems under minimax rules. Based on the uncertainty of the expected return of securities, therefore, it is of significant and interesting to study portfolio models based on fuzzy interval numbers under minimax rules(in briefly, PMFM). This PMFM-model can be regarded as a natural generalization of ordinarily portfolio model ...

We provide a complete picture of asymptotically minimax estimation of Lr-norms (for any r ≥ 1) of the mean in Gaussian white noise model over Nikolskii-Besov spaces. In this regard, we complement the work of Lepski, Nemirovski and Spokoiny (1999), who considered the cases of r = 1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bo...

Linear ?-minimax estimators for a bounded normal mean have been explored by Vidakovic and DasGupta (1992). They have found that the risk of linear ?-minimax rules is close to the risk of exact ?-minimax rules. However, the linear rules are not very natural when one estimates bounded parameters. In this paper we explore some modiications of linear rules with two goals in mind: (i) addressing the...

Minimax is the basic algorithm used in two-persons player complete information computer games. It is also used in other games. Early research on the MiniMax algorithm have improved it giving the Alpha-Beta algorithm. We propose a list of program transformations that enable to rediscover the Alpha-Beta algorithm given the original MiniMax algorithm. This example is intended to serve as a basis f...

We consider an infinite-horizon linear-quadratic minimax optimal control problem for stochastic uncertain systems with output measurement. A new description of stochastic uncertainty is introduced using a relative entropy constraint. For the stochastic uncertain system under consideration, a connection between the worst-case control design problem and a specially parametrized risk-sensitive sto...