Michael R. Capalbo

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The main concrete result of this paper is the first explicit construction of constant degree <i>lossless</i> expanders. In these graphs, the expansion factor is almost as large as possible: (1&#8212;&#949;)<i>D</i>, where <i>D</i> is the degree and &#949; is an arbitrarily small constant. The best previous explicit constructions gave expansion factor D/2,(More)
The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: , where is the degree and is an arbitrarily small constant. Such graphs are essential components in networks that can implement fast distributed, routing algorithms e.g. [PU89,(More)
Let H be a family of graphs. A graph T is H-universal if it contains a copy of each H ∈ H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For all positive integers k and n, we construct an H(k, n)-universal graph T with Ok(n 2 k log 4 k n) edges and exactly n vertices. The number of edges is almost as(More)
For any positive integers and , let denote the family of graphs on vertices with maximum degree , and let denote the family of bipartite graphs on vertices with vertices in each vertex class, and with maximum degree . On one hand, we note that any -universal graph must have edges. On the other hand, for any , we explicitly construct -universal graphs and on(More)
Let H be a family of graphs. We say that G is H-universal if, for each H ∈ H, the graph G contains a subgraph isomorphic to H. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For each fixed k and each n sufficiently large, we explicitly construct an H(k, n)-universal graph Γ (k, n) with O(n(log n)) edges. This is optimal(More)
We present a simple, explicit construction of an infinite family F of bounded-degree ’unique-neighbor’ expanders Γ; i.e., there are strictly positive constants α and , such that all Γ = (X,E(Γ)) ∈ F satisfy the following property. For each subset S of X with no more than α|X| vertices, there are at least |S| vertices in X \ S that are adjacent in Γ to(More)
We describe a deterministic, polynomial time algorithm for finding edge-disjoint paths connecting given pairs of vertices in an expander. Specifically, the input of the algorithm is a sufficiently strong d-regular expander G on n vertices, and a sequence of pairs s<sub>i</sub>, t<sub>i</sub> (1lesilesr) of vertices, where, r=Theta(nd log d/log n), and no(More)
Pseudorandomness is the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This survey of the subject places particular emphasis on the intimate connections that have been discovered between a variety of fundamental “pseudorandom objects” that at first seem very different in nature: expander(More)