Let a Golomb ruler be a set of integers so that all absolute values of differences between any two marks are distinct. An order 2 Golomb ruler is a Golomb ruler such that all absolute values of differences of differences between any pair of marks, are distinct as much as possible. Contruction of optimum order 2 Golomb ruler, i.e., of rulers of minimum length, is a highly combinatorial problem which has applications, e.g., in the design of convolutional self doubly orthogonal codes. We propose here a first exact algorithm, different from a pure exhaustive search, for building optimum order 2 Golomb rulers and provide new rulers which improve on the previous ones for up to 20 marks.

WDM networks are telecommunication networks of great capacity based on optical technologies. It is a very attractive medium for networks that carry high transmission rate, an enormous bandwidth is available on a fiber and the same fiber can be used for multiple data streams. One of the challenging optimization problem in WDM networks deals with the routing and wavelength assignment problem. Given a set of connection requests (static routing) and the number of available wavelengths the fiber supports on each link, we are to find through the network a route for each request and assign wavelength (or wavelengths depending on the hypothesis on the routers and switching nodes) to them. Several algorithms and approaches have already been proposed in the literature. We here propose a new two-phase algoirhtm that corresponds to an interlaced two-phase procedure and compare its results with previous computational results of the literature.

Mobile ad hoc networks (often referred to as MANETs) consist of wireless hosts that communicate with each other in the absence of a fixed infrastructure. They are used in disaster relief, conference and battlefield environments, and are currently receiving a significant attention. A central challenge in the design of MANETs is the development of routing protocols that can efficiently find routes between two communicating nodes. The routing protocol must be able to keep up with the high degree of mobility that often changes the network topology drastically and unpredictably. We will present of survey of the current routing protocols and discuss their avantages and disadvantages.

The Golomb ruler problem consists in finding n integers such that all possible differences are distinct and such that the largest difference is minimized. Three lower bounds based on linear programming have been proposed in the literature for this problem. We prove that they have all the same value. We also show that a natural strengthening of these linear formulations does not succeed to improve the value of these lower bounds.