Joel H. Spencer

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The use of randomness is now an accepted tool in Theoretical Computer Science but not everyone is aware of the underpinnings of this methodology in Combinatorics - particularly, in what is now called the probabilistic Method as developed primarily by Paul Erdo&huml;s over the past half century. Here I will explore a particular set of problems - all dealing(More)
Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and(More)
18 until the number of vertices left is O(n=d), and color the remaining vertices in an arbitrary manner. 7. The existence of an approximation algorithm based on the spectral method for coloring arbitrary graphs is a question that deserves further investigation (which we do not address here.) Recently, improved approximation algorithms for graph coloring(More)
<lb>We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite<lb>graph and analyze the algorithm using the theory of discrete time random processes. As a result<lb>we obtain a simple criterion invovlving the fractions of nodes of di erent degrees on both sides of<lb>the graph which is necessary and su cient for the(More)