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Max-plus methods have previously been used to solve deterministic control problems. The methods are based on max-plus (or min-plus) expansions and can yield curse-of-dimensionalityfree numerical methods. In this paper, we explore min-plus methods for continuous-time stochastic control on a finite-time horizon. We first approximate the original value function via timediscretization. By generalizing the min-plus distributive property to continuum spaces, we obtain an algorithm for recursive computation of the time-discretized values, which we refer to as the idempotent distributed dynamic programming principle (IDDPP). Under the IDDPP, the value function at each step can be represented as an infimum of functions in a certain class. This is a min-plus expansion for the value function. For the specific class of problems considered here, we see that the class can be taken as that consisting of the quadratic functions. A means for reducing the numbers of constituent quadratic functions is discussed. [ABSTRACT FROM AUTHOR]

This paper shows how to compute O(√log n)-approximations to the Sparsest Cut and Balanced Separator problems in Õ(n²) time, thus improving upon the recent algorithm of Arora, Rao, and Vazirani [Proceedings of the 36th Annual ACM Symposium on Theory of Computing, 2004, pp. 222-231]. Their algorithm uses semidefinite programming and requires Õ (n9.5) time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander flows was also established by Arora, Rao, and Vazirani. [ABSTRACT FROM AUTHOR]

In this paper we study a discrete version of the classical team decision problem. It has been shown previously that the general discrete team decision problem is NP-hard. Here we present an efficient approximation algorithm for this problem. For the maximization version of this problem with nonnegative rewards, this algorithm computes decision rules which are guaranteed to be within a fixed bound of optimal. [ABSTRACT FROM AUTHOR]