The Automatic Identification System (AIS) is extensively used in monitoring vessel traffic, and ship navigation related information can be obtained from the AIS data. However, AIS data contain extensive redundant information, which leads to the general need to compress the data when applying it in practice or conducting research. In this paper, a three-dimensional compression of ship trajectories using the Dynamic Programming algorithm has been proposed. The AIS data near the ports of Long Beach and San Francisco in the United States were used to test and compare the Dynamic Programming algorithm with the Top-down Time-ratio algorithms. The experimental results show that the proposed algorithm can better retain the position and time information at low compression ratio such as 1%, 20% and 40%. Moreover, the algorithm is applicable to ship trajectories with different motion modes such as steering, mooring and straight ahead. The results show that the proposed algorithm can reasonably solve the problem of AIS data redundancy and ensure the quality of data, which is of practical significance for water transport, transport planning and other related research.

Given a finite collection of strings of letters from a fixed alphabet, it is of interest, in the contexts of data compression and DNA sequencing, to find the length of the shortest string which contains each of the given strings as a consecutive substring. In order to analyze the average behavior of the optimal superstring length, substrings of specified lengths are considered with the letters selected independently at random. An asymptotic expression is obtained for the savings from compression, i.e. the difference between the uncompressed (concatenated) length and the optimal superstring length.

We present a systematic method of approximating, to an arbitrary accuracy, a probability measure µ on x = [0,1]q, q 1, with invariant measures for iterated function systems by matching its moments. There are two novel features in our treatment. 1. An infinite set of fixed affine contraction maps on , w2, · ·· }, subject to an ‘ϵ-contractivity' condition, is employed. Thus, only an optimization over the associated probabilities pi is required. 2. We prove a collage theorem for moments which reduces the moment matching problem to that of minimizing the collage distance between moment vectors. The minimization procedure is a standard quadratic programming problem in the pi which can be solved in a finite number of steps. Some numerical calculations for the approximation of measures on [0, 1] are presented.