We consider dictionaries that perform lookups by probing a single word of memory, knowing only the size of the data structure. We describe a randomized dictionary where a lookup returns the correct answer with probability 1− , and otherwise returns “don’t know”. The lookup procedure uses an expander graph to select the memory location to probe. Recent explicit expander constructions are shown t...

We consider the task of interconnecting processors to realize efficient parallel algorithms. We propose interconnecting processors using certain graphs called expander graphs, which can provide fast communication from any group of processors to the rest of the network. We show that these interconnections would result in a number of efficient parallel algorithms for sorting, routing, associative...

Now, it is easy to see from the definition that a complete graph is definitely an edge expander as per the above definition. For our applications, we will be mostly interested in expander graphs which have a much smaller number of edges. For example, we would be interested in d-regular graphs which are expanders with parameters d = O(1) and α = θ(1). Clearly, α cannot exceed d. The existence of...

In this survey we review basic facts regarding expander graphs that are most relevant to the theory of computation.

In this paper, we calculate optimal prism configurations for achromatic N-prism beam expanders of a single material; we argue that for moderate to high magnifications, that is, M > [2 1(2N-1 -1)]N, the upup ... up-down configuration is generally optimal, in the sense that it maximizes the transmission for given magnification. We also derive exact expressions for the incidence and apex angles th...

We give a fully combinatorial analysis (using edge expansion) of an iterative expander construction due to Reingold, Vadhan, and Wigderson [RVW02]. This shows that both the construction of constantdegree expanders and its analysis can be carried out using only elementary combinatorial tools.

a complete diet (total mixed ration) with sorghum stover (40%) as sole roughage source was prepared and offered to animals under two forms: as mash or as expanded-extruded pellets (eep). these two complete diets were compared with a conventional diet (ad libitum chopped sorghum stover fed separately with concentrate mixture to meet 80% of protein requirements). these three diets were randomly a...

PurPoSe: Acellular dermal matrix (ADM) has gained popularity to enhance lower pole coverage in immediate implant or expander reconstruction. Advantages of ADM include improved rapid reconstruction, postoperative expander filling and lower capsular contracture. Potential trade-offs include higher seroma, infection and cost. Alternatives for implant coverage include local fascial flaps and inferi...

Random walks on graphs have turned out to be a powerful tool in the design of algorithms and other applications. In particular, expander graphs, which are graphs on which random walks have particularly good properties, are extremely useful in complexity and other areas of computer science. In this chapter we study random walks on general regular graphs, leading to a the randomized logspace algo...

Random walks on graphs have turned out to be a powerful tool in the design of algorithms and other applications. In particular, expander graphs, which are graphs on which random walks have particularly good properties, are extremely useful in complexity and other areas of computer science. In this chapter we will study random walks on general graphs, leading to a the randomized logspace algorit...