Nathan Linial

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This paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion. The computational model is such that each node of the graph is occupied by a processor which has its own ID. Processors are restricted to collecting data from others which are at a distance at most away from them in time units, but are(More)
In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspect ive on a number of graph-theoret ic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometr ic representa t ions tha t respect the metric of the (possibly weighted) graph.(More)
In this paper, Boolean functions in ,4C0 are studied using harmonic analysis on the cube. The main result is that an ACO Boolean function has almost all of its “power spectrum” on the low-order coefficients. An important ingredient of the proof is Hastad’s switching lemma [8]. This result implies several new properties of functions in -4C[’: Functions in(More)
A radio network is a synchronous network of processors that communicate by transmitting messages to their neighbors, where a processor receives a message in a given step if and only if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove the existence of a family of radius-2 networks on n vertices for which any(More)
What is the largest number of edges in a graph of order n and girth g? For dregular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an affirmative answer to an old open problem ([4] p.163, problem 10). What is the maximal number of edges in a graph with n(More)
In practice, almost all dynamic systems require decisions to be made on-line, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general on-line decision algorithm is developed. It is shown that, for an important class of special cases, this algorithm is optimal among(More)