Optimal point-to-point broadcast algorithms via lopsided trees

Optimal point-to-point broadcast algorithms via lopsided trees

Optimal Algorithms to Embed Trees in a Point Set

We present optimal Θ(n log n) time algorithms to solve two tree embedding problems whose solution previously took quadratic time or more: rooted-tree embeddings and degree-constrained embeddings. In the rootedtree embedding problem we are given a rooted tree T with n nodes and a set of n points P with one designated point p and are asked to find a straight-line embedding of T into P with the ro...

Journal of Graph Algorithms and Applications Optimal Algorithms to Embed Trees in a Point Set

We present optimal (n log n) time algorithms to solve two tree embedding problems whose solution previously took quadratic time or more: rooted-tree embeddings and degree-constrained embeddings. In the rootedtree embedding problem we are given a rooted tree T with n nodes and a set of n points P with one designated point p and are asked to nd a straight-line embedding of T into P with the root ...

Lopsided Trees: Analyses, Algorithms, and Applications

Lopsided trees are rooted, ordered, trees in which the length of an edge from a node to its i th child depends upon the value of i: These trees model a variety of problems and have therefore been extensively studied. In this paper we combine analytic and combinatorial techniques to address three open problems on such trees: Given n, eeciently construct a lopsided tree with n leaves that has min...

Expressiveness of Point-to-Point versus Broadcast Communications