For many applications of location-based services, such as friend finding, buddy tracking,information sharing and cooperative caching in ad hoc networks, it is often important to be able to identify whether the positions of a given set of moving objects are within close proximity. To compute these kinds of proximity relations among large populations of moving objects, continuously available location position information of these objects must be correlated against each other to identify whether a given set of objects are in the specified proximity relation. In this dissertation, we state this problem, referring to it as the location constraint matching problem, both in the Euclidean space and the road network space. In the Euclidean space, we present an adaptive solution to this problem for various environments. We also study the position uncertainty associated with the constraint matching. For the road network space, where the object can only move along the edges of the road network, we propose an efficient algorithm based on graph partitioning, which dramatically restricts the search space and enhances performance. Our approaches reduce the constraint processing time by 80% for Euclidean space and by 90% for road network space respectively. The logical combination of individual constraints with conjunction, disjunction and negation results in more expressive constraint expressions than are possible based on single constraints. We model constraint expressions with Binary Decision Diagrams (BDD). Furthermore, we exploit the shared execution of constraint combinations based on the BDD modeling. All the algorithms for various aspects of the constraint processing are integrated in the research prototype L-ToPSS (Location-based Toronto Publish/Subscribe System). Through experimental study and the development of an analytical model, we show that the proposed solution scales to large numbers of constraints and large numbers of moving objects.

For many applications of location-based services, such as friend finding, buddy tracking,information sharing and cooperative caching in ad hoc networks, it is often important to be able to identify whether the positions of a given set of moving objects are within close proximity. To compute these kinds of proximity relations among large populations of moving objects, continuously available location position information of these objects must be correlated against each other to identify whether a given set of objects are in the specified proximity relation. In this dissertation, we state this problem, referring to it as the location constraint matching problem, both in the Euclidean space and the road network space. In the Euclidean space, we present an adaptive solution to this problem for various environments. We also study the position uncertainty associated with the constraint matching. For the road network space, where the object can only move along the edges of the road network, we propose an efficient algorithm based on graph partitioning, which dramatically restricts the search space and enhances performance. Our approaches reduce the constraint processing time by 80% for Euclidean space and by 90% for road network space respectively. The logical combination of individual constraints with conjunction, disjunction and negation results in more expressive constraint expressions than are possible based on single constraints. We model constraint expressions with Binary Decision Diagrams (BDD). Furthermore, we exploit the shared execution of constraint combinations based on the BDD modeling. All the algorithms for various aspects of the constraint processing are integrated in the research prototype L-ToPSS (Location-based Toronto Publish/Subscribe System). Through experimental study and the development of an analytical model, we show that the proposed solution scales to large numbers of constraints and large numbers of moving objects.

We propose interval arithmetic and interval constraint algorithms for global optimization. Both of these compute lower and upper bounds of a function over a box, and return a lower and an upper bound for the global minimum. In interval arithmetic methods, the bounds are computed using interval arithmetic evaluations. Interval constraint methods instead use domain reduction operators and consistency algorithms. The usual interval arithmetic algorithms for global optimization suffer from at least one of the following drawbacks: - Mixing the fathoming problem, in which we ask for the global minimum only, with the localization problem, in which we ask for the set of points at which the global minimum occurs. - Not handling the inner and outer approximations for epsilon-minimizer, which is the set of points at which the objective function is within epsilon of the global minimum. - Nothing is said about the quality for their results in actual computation. The properties of the algorithms are stated only in the limit for infinite running time, infinite memory, and infinite precision of the floating-point number system. To handle these drawbacks, we propose interval arithmetic algorithms for fathoming problems and for localization problems. For these algorithms we state properties that can be verified in actual executions of the algorithms. Moreover, the algorithms proposed return the best results that can be computed with given expressions for the objective function and the conditions, and a given hardware. Interval constraint methods combine interval arithmetic and constraint processing techniques, namely consistency algorithms, to obtain tighter bounds for the objective function over a box. The basic building block of interval constraint methods is the generic propagation algorithm. This explains our efforts to improve the generic propagation algorithm as much as possible. All our algorithms, namely dual, clustered, deterministic, and selective propagation algorithms, are developed as an attempt to improve the efficiency of the generic propagation algorithm. The relational box-consistency algorithm is another key algorithm in interval constraints. This algorithm keeps squashing the left and right bounds of the intervals of the variables until no further narrowing is possible. A drawback of this way of squashing is that as we proceed further, the process of squashing becomes slow. Another drawback is that, for some cases, the actual narrowing occurs late. To address these problems, we propose the following algorithms: - Dynamic Box-Consistency algorithm: instead of pruning the left and then the right bound of each domain, we alternate the pruning between all the domains. - Adaptive Box-Consistency algorithm: the idea behind this algorithm is to get rid of the boxes as soon as possible: start with small boxes and extend them or shrink them depending on the pruning outcome. This adaptive behavior makes this algorithm very suitable for quick squashing. Since the efficiency of interval constraint optimization methods depends heavily on the sharpness of the upper bound for the global minimum, we must make some effort to find the appropriate point or box to use for computing the upper bound, and not to randomly pick one as is commonly done. So, we introduce interval constraints with exploration. These methods use non-interval methods as an exploratory step in solving a global optimization problem. The results of the exploration are then used to guide interval constraint algorithms, and thus improve their efficiency.