Abstract: .We present a new methodology for computing approximate
Nash equilibria for two-person non-cooperative games based upon certain
extensions and specializations of an existing optimization approach pre-
viously used for the derivation of xed approximations for this problem.
In particular, the general two-person problem is reduced to an inde-
nite quadratic programming problem of special structure involving the
n x n adjacency matrix of an induced simple graph specied by the in-
put data of the game, where n is the number of players' strategies.
Abstract: Urban road networks are represented as directed graphs, accompanied by a metric which assigns cost functions (rather than scalars) to the arcs, e.g. representing time-dependent arc-traversal-times. In this work, we present oracles for providing time-dependent min-cost route plans, and conduct their experimental evaluation on a real-world data set (city of Berlin). Our oracles are based on precomputing all landmark-to-vertex shortest travel-time functions, for properly selected landmark sets. The core of this preprocessing phase is based on a novel, quite efficient and simple oneto-all approximation method for creating approximations of shortest travel-time functions. We then propose three query algorithms, including a PTAS, to efficiently provide mincost route plan responses to arbitrary queries. Apart from the purely algorithmic challenges, we deal also with several
implementation details concerning the digestion of raw traffic data, and we provide heuristic improvements of both the preprocessing phase and the query algorithms. We conduct an extensive, comparative experimental study with all query algorithms and six landmark sets. Our results are quite encouraging, achieving remarkable speedups (at least by two orders of magnitude) and quite small approximation guarantees, over the time-dependent variant of Dijkstra˘s algorithm.
Abstract: This paper addresses stability issues in incremental induction of decision trees. Stability problems arise when an induction algorithm must revise a decision tree very often and oscillations between similar concepts decrease learning speed. We review a heuristic that solves this problem and subsequently employ asymptotic analysis to approximate the basic parameters related to the estimation of computational effort in incremental learning of decision trees. We then use these approximations to simplify the heuristic, we deliver insight into its amortizing behavior and argue how they can also speed-up its execution and enhance its applicability, also providing experimental evidence to support these claims.