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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)
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)
It is proved that there are constants cl, c2, and c3 such that for any set S of n points in the unit square and for any minimum-length tour T of S (1) the sum of squares of the edge lengths of T is bounded by Cl logn. (2) the number of edges having length or greater in T is at most c2/t 2, and (3) the sum of edge lengths of any subset E of T is bounded by(More)