Lower bounds for Minimum Interference Frequency Assignment Problems (original) (raw)

Optimal Solutions for Frequency Assignment Problems via Tree Decomposition

Lecture Notes in Computer Science, 1999

In this paper we describe a computational study to solve hard frequency assignment problems (FAPs) to optimality using a tree decomposition of the graph that models interference constraints. We present a dynamic programming algorithm which solves FAPs based on this tree decomposition. With the use of several dominance and bounding techniques it is possible to solve small and medium-sized real-life instances of the frequency assignment problem to optimality. Moreover, with an iterative version of the algorithm we obtain good lower bounds for large-sized instances within reasonable time and memory limits.

Upper and lower bounding techniques for frequency assignment problems

We consider two v ariants of the radio link frequency assignment problem. These problems arise in practice when a network of radio links has to be established. Each radio link has to be assigned a particular frequency. T h e i n terference level between the frequencies assigned to the di erent links has to be acceptable, since otherwise communication will be distorted. The frequency assignments have to comply with certain regulations and physical characteristics of the transmitters. Moreover, the number of frequencies is to be minimized, because each frequency used in the network has to be reserved at a certain cost. We d e v elop several approximation algorithms for the problems, which are based on local search, and we compare their performance on some practical instances. Lower bounding techniques based on nonlinear programming and the chromatic number of a graph are used to estimate the quality of the approximate solutions for these instances.

Models and methods for frequency assignment with cumulative interference constraints

International Transactions in Operational Research, 2008

In this paper, a realistic modeling of interferences for frequency assignment in hertzian telecommunication networks is presented. In contrast with traditional interference models based only on binary interference constraints involving two frequencies, this new approach considers the case of cumulative disruptions that are modeled through a unique non-binary constraint. To deal with these complex constraints, we propose extensions of classical integer linear programming formulations. On a set of realistic instances, we propose hybrid constraint programming and large neighborhood search solution methods to solve minimum interference and minimum span frequency assignment problems. We compare their performances with those of existing heuristics. Finally, we show how the end-user benefits from using the cumulative model instead of the traditional one.

Models and solution techniques for the frequency assignment problem

2003

Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, andmilitary operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion. This survey gives an overview of the models and methods that the literature provides on the topic. We present a broad description of the practical settings in which frequency assignment is applied. We also present a classification of the different models and formulations described in the literature, such that the common features of the models are emphasized. The solution methods are divided in two parts. Optimization and lower bounding techniques on the one hand, and heuristic search techniques on the oth...

A branch-and-cut algorithm for the frequency assignment problem

The frequency assignment problem FAP is the problem of assigning frequencies to transmission links such that no interference between signals occurs. This implies distance constraints between assigned frequencies of links. The objective is to minimize the number of used frequencies. We present a n i n teger linear programming formulation that is closely related to the vertex packing problem. Although the size of this formulation is an order of magnitude larger than the underlying network of links, we use the integer linear programming formulation within a branch-and-cut algorithm. This algorithm employs problem speci c and generic techniques such as reduction methods, primal heuristics, and branching rules to obtain optimal solutions. We report on computational experience with real-life instances.

Models and Solution Techniques for Frequency Assignment Problems: updated

Annals of Operations Research, 2007

Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion.

Models and solution techniques for frequency assignment problems

A Quarterly Journal of Operations Research, 2003

Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion. This survey gives an overview of the models and methods that the literature provides on the topic. We present a broad description of the practical settings in which frequency assignment is applied. We also present a classification of the different models and formulations described in the literature, such that the common features of the models are emphasized. The solution methods are divided in two parts. Optimization and lower bounding techniques on the one hand, and heuristic search techniques on the other hand. The literature is classified according to the used methods. Again, we emphasize the common features, used in the different papers. The quality of the solution methods is compared, whenever possible, on publicly available benchmark instances.

An improved algorithm to determine lower bounds for the fixed spectrum frequency assignment problem

2004

Frequencies have to be assigned to transmitters whenever a radio network is established or modified. This is ideally done is a way which minimises interference in the network. Lower bounds are necessary to establish the effectiveness of the heuristic algorithms used for this task and to assess the quality of the assignments obtained. In the fixed spectrum frequency assignment problem the available frequencies are known in advance.