Abstract We introduce the notion of a Utilitarian Postman (UP) path on a network Q as one which minimizes the expected time required to find a random (uniformly distributed) point, and show that UP paths must be used in a minimax search of a symmetric network. For any network Q, one may consider the zero‐sum search game Γ(Q) in which the (minimizing) Searcher picks a unit speed path S(t) in Q, the Hider picks a point H in Q, and the payoff is the meeting time T = min{t : S(t) = H}. We show first that if Q is symmetric (edge and vertex transitive), then it is optimal for the Hider to pick H uniformly in Q, so that the Searcher must follow a UP path. We then show that if Q is symmetric of odd degree, with n vertices and m unit length edges, the value V of Γ(Q) satisfies $ V \geq {m \over 2} + {n^{2}-2n \over 8m} $ , with equality if and only if (*): Q has a path P = v1, v2,…,vn−1 of distinct vertices, such that the edge set Q′ = Q−∪ (v2i,v2i+1) is connected. In this case, there is a UP path for Q consisting of P followed by an Eulerian path E of Q′. The condition (*) is satisfied by many symmetric graphs, including all complete graphs, complete bipartite graphs, hypercube graphs, high valency graphs, and the Petersen graph. We know of no odd degree symmetric graph not satisfying (*). © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

Abstract We analyze a zero‐sum game between a blind unit‐speed searcher and a stationary hider on a given network Q, where the payoff is the time for the searcher to reach the hider. In contrast to the standard game studied in the literature, we do not assume that the searcher has to start from a fixed point (known to the hider) but can choose his starting point. We show that for some networks, including trees, the optimal searcher, and hider strategies have a simple structure. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the “accurate tables method.” This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all arguement values. Our main idea in the accurate tables method is to use “nonstandard tables,” which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double percision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

This correspondence considers the efficiency of some algorithms for the evaluation of monotonic Boolean functions. It is shown that algorithms based on the criterion of maximizing the local information gain about the Boolean function with n variables may sometimes require a number of computational steps which is n/log n times the computational steps of the optimal algorithm.