Obtaining a matching in a graph satisfying a certain objective is an important class of graph problems. Matching algorithms have received attention for several decades. However, while there are efficient algorithms to obtain a maximum weight matching, not much is known about the maximum weight maximum cardinality, and maximum cardinality maximum weight matching problems for general graphs. Our contribution in this work is to show that for bounded weight input graphs one can obtain an algorithm for both maximum weight maximum cardinality (for real weights), and maximum cardinality maximum weight matching (for integer weights) by modifying the input and running the existing maximum weight matching algorithm. Also, given the current state of the art in maximum weight matching algorithms, we show that, for bounded weight input graphs, both maximum weight maximum cardinality, and maximum cardinality maximum weight matching have algorithms of similar complexities to that of maximum weight matching. Subsequently, we also obtain approximation algorithms for maximum weight maximum cardinality, and maximum cardinality maximum weight matching.

The ease of deployment and the low cost of static adhoc wireless sensor networks, make them an ideal infrastructure of choice for various monitoring applications. The flexibility of expressing meaningful queries in terms of userdefined regions form an important goal of any such monitoring and query framework. Towards efficient implementation of that goal, we emphasize upon the need for supporting application-defined regions, in contrast to network driven automatic cluster-formations (either flat or hierarchical -which are typically query-agnostic).

No abstract

No abstract