We show that the combinatorial complexity of the union of n infinite cylinders in R3 , having arbitrary radii, is O(n2+ε ), for any ε > 0; the bound is almost tight in the w...
We address the issue of inapproximability of the wavelength assignment problem in wavelength division multiplexing (WDM) optical networks. We prove that in an n-node WDM optical ne...
The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey theory in combinatorics. Gi...
We consider the problem of embedding a metric into low-dimensional Euclidean space. The classical theorems of Bourgain, and of Johnson and Lindenstrauss say that any metric on n p...
We prove that approximating the Max Acyclic Subgraph problem within a factor better than 1/2 is Unique-Games hard. Specifically, for every constant ε > 0 the following holds:...