Improved Sparse Covers for Graphs Excluding a Fixed Minor Costas Busch Ryan LaFortune Srikanta Tirthapura We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the °-neighborhood of each node. For planar graphs, the cover has radius no more than 24° ¡ 8 and degree (maximum cluster overlap) no more than 30. The radius and degree are optimal up to constant factors. For every n node graph that excludes a fixed minor, we present an algorithm that yields a cover with radius no more than 4° and degree O(log n). This is a significant improvement over previous results for planar graphs and for graphs excluding a fixed minor; in order to obtain clusters with radius of O(°), it was required to have degree polynomial in n. Since sparse covers have many applications in distributed computing, including compact routing, distributed directories and synchronizers, our improved cover construction results in improved algorithms for all these problems, for the class of minor-free graphs. Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY cs-06-16
Improved Sparse Covers for Graphs Excluding a Fixed Minor
Costas Busch
Ryan LaFortune
Srikanta Tirthapura
We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the °-neighborhood of each node. For planar graphs, the cover has radius no more than 24° ¡ 8 and degree (maximum cluster overlap) no more than 30. The radius and degree are optimal up to constant factors. For every n node graph that excludes a fixed minor, we present an algorithm that yields a cover with radius no more than 4° and degree O(log n). This is a significant improvement over previous results for planar graphs and for graphs excluding a fixed minor; in order to obtain clusters with radius of O(°), it was required to have degree polynomial in n. Since sparse covers have many applications in distributed computing, including compact routing, distributed directories and synchronizers, our improved cover construction results in improved algorithms for all these problems, for the class of minor-free graphs.
Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY
cs-06-16