Channel assignment in cellular radio

Some heuristic channel-assignment algorithms for cellular systems are described. These algorithms have yielded optimal, or near-optimal assignments, in many cases. The channel-assignment problem can be viewed as a generalized graph-coloring problem, and these algorithms have been developed, in part, by suitably adapting some of the ideas previously introduced in heuristic graph-coloring algorithms. The channel-assignment problem is formulated as a minimum-span problem, i.e. a problem wherein the requirement is to find the minimum bandwidth necessary to satisfy a given demand. Examples are presented, and algorithm performance results are discussed

Multi-Channel Scheduling for Fast Convergecast in Wireless Sensor Networks

We explore the following fundamental question - how fast can information be collected from a wireless sensor network? We consider a number of design parameters such as, power control, time and frequency scheduling, and routing. There are essentially two factors that hinder efficient data collection - interference and the half-duplex single-transceiver radios. We show that while power control helps in reducing the number of transmission slots to complete a convergecast under a single frequency channel, scheduling transmissions on different frequency channels is more efficient in mitigating the effects of interference (empirically, 6 channels suffice for most 100-node networks). With these observations, we define a receiver-based channel assignment problem, and prove it to be NP-complete on general graphs. We then introduce a greedy channel assignment algorithm that efficiently eliminates interference, and compare its performance with other existing schemes via simulations. Once the interference is completely eliminated, we show that with half-duplex single-transceiver radios the achievable schedule length is lower-bounded by max(2nk − 1,N), where nk is the maximum number of nodes on any subtree and N is the number of nodes in the network. We modify an existing distributed time slot assignment algorithm to achieve this bound when a suitable balanced routing scheme is employed. Through extensive simulations, we demonstrate that convergecast can be completed within up to 50% less time slots, in 100-node networks, using multiple channels as compared to that with single-channel communication. Finally, we also demonstrate further improvements that are possible when the sink is equipped with multiple transceivers or when there are multiple sinks to collect data

Acyclic orientations with path constraints

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities

A general framework for coloring problems: old results, new results, and open problems

In this survey paper we present a general framework for coloring problems that was introduced in a joint paper which the author presented at WG2003. We show how a number of different types of coloring problems, most of which have been motivated from frequency assignment, fit into this framework. We give a survey of the existing results, mainly based on and strongly biased by joint work of the author with several different groups of coauthors, include some new results, and discuss several open problems for each of the variants

Automatic frequency assignment for cellular telephones using constraint satisfaction techniques

We study the problem of automatic frequency assignment for cellular telephone systems. The frequency assignment problem is viewed as the problem to minimize the unsatisfied soft constraints in a constraint satisfaction problem (CSP) over a finite domain of frequencies involving co-channel, adjacent channel, and co-site constraints. The soft constraints are automatically derived from signal strength prediction data. The CSP is solved using a generalized graph coloring algorithm. Graph-theoretical results play a crucial role in making the problem tractable. Performance results from a real-world frequency assignment problem are presented. We develop the generalized graph coloring algorithm by stepwise refinement, starting from DSATUR and augmenting it with local propagation, constraint lifting, intelligent backtracking, redundancy avoidance, and iterative deepening