2 J ul 2 00 1 Orderly Spanning Trees with Applications ∗ Hsueh -

Orderly Spanning Trees with Applications

We introduce and study orderly spanning trees of plane graphs. This algorithmic tool generalizes canonical orderings, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an orderly pair for any connected planar graph G, consisting of an embedded planar graph H isomorphic to G, and an orderly spanning ...

Compact Floor-Planning via Orderly Spanning Trees

Floor-planning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)-time algorithm to construct a floorplan for any n-node plane triangulation. In comparison with previous floor-planning algorithms in the literature, our solution is not only simpler in the algorithm itself, but also produces floor-plans which require fewer module ...

Floor-Planning via Orderly Spanning Trees

Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees

We address the problem of designing compact routing tables for an unlabeled connected n-node planar network G. For each node r of G, the designer is given a routing spanning tree Tr of G rooted at r, which specifies the routes for sending packets from r to the rest of G. Each node r of G is equipped with ports 1, 2, . . . , degr, where degr is the degree of r in Tr . Each port of r is supposed ...

Congestion-free embedding of 2(n-k) spanning trees in an arrangement graph

The arrangement graph An;k is not only a generalization of star graph (nÿ k ˆ 1), but also more ̄exible. In this investigation, we elucidate the problem of embedding of multiple spanning trees in an arrangement graph with the objective of congestion-free. This result is to report how to exploit 2…nÿ k† edge disjoint spanning trees in an arrangement graph, where each congestion-free spanning tre...