Anna Östlin

Deterministic Radio Broadcasting

We consider broadcasting in radio networks: one node of the network knows a message that needs to be learned by all the remaining nodes. We seek distributed deterministic algorithms to perform this task. Radio networks are modeled as directed graphs. They are unknown, in the sense that nodes are not assumed to know their neighbors, nor the size of the network, they are aware only of their individual identifying numbers. If more than one message is delivered to a node in a step then the node cannot hear any of them. Nodes cannot distinguish between such collisions and the case when no messages have been delivered in a step. The fastest previously known deterministic algorithm for deterministic distributed broadcasting in unknown radio networks was presented in [6], it worked in time O(n11/6). We develop three new deterministic distributed algorithms. Algorithm A develops further the ideas of [6] and operates in time O(n1:77291) = O(n9/5), for general networks, and in time O(n1+a+H(a)+o(1)) for sparse networks with in-degrees O(na) fora < 1=2; here H is the entropy function. Algorithm B uses a new approach and works in time O(n3/2 log1/2 n) for general networks or O(n1+a+o(1)) for sparse networks. Algorithm C further improves the performance for general networks running in time O(n3/2).

Uniform hashing in constant time and linear space

Many algorithms and data structures employing hashing have been analyzed under the uniform hashing assumption, i.e., the assumption that hash functions behave like truly random functions. Starting with the discovery of universal hash functions, many researchers have studied to what extent this theoretical ideal can be realized by hash functions that do not take up too much space and can be evaluated quickly. In this paper we present an almost ideal solution to this problem: A hash function that, on any set of n inputs, behaves like a truly random function with high probability, can be evaluated in constant time on a RAM, and can be stored in O(n) words, which is optimal. For many hashing schemes this is the first hash function that makes their uniform hashing analysis come true, with high probability, without incurring overhead in time or space.

On the complexity of constructing evolutionary trees

AbstractIn this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of

Efficient Merging, Construction, and Maintenance of Evolutionary Trees

N^\varepsilon

The Complexity of Constructing Evolutionary Trees Using Experiments

, where N is the input size, for any 0 ≤

Efficient Merging and Construction of Evolutionary Trees

\varepsilon < \tfrac{1}{9}