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Let Xf, 1 < i < 00, be unifonnly distributed in [0, if and let T " be the length of the shortest closed path ccmaecting {Xf,X2,. .. , X "). \t is proved that there is a constant 0< ;8< oo such that for all o 0 This result is esseatial in Justifying Karp's algorithm for the trav«UtBg saksman problrai under the independent model, and it settles a question… (More)

- J Michael Steele
- 2002

The theory of the minimal spanning tree (MST) of a connected graph whose edges are assigned lengths according to independent identically distributed random variables is developed from two directions. First, it is shown how the Tutte polynomial for a connected graph can be used to provide an exact formula for the length of the minimal spanning tree under the… (More)

We identify a rich class of finite-horizon Markov decision problems (MDPs) for which the variance of the optimal total reward can be bounded by a simple affine function of its expected value. The class is characterized by three natural properties: reward boundedness, existence of a do-nothing action, and optimal action monotonicity. These properties are… (More)