Sampling conditions for recovering the homology of a set using topological persistence are much weaker than sampling conditions required by any known algorithm for producing a top...
We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n)....
Every compact orientable boundaryless surface M can be cut along simple loops with a common point v0, pairwise disjoint except at v0, so that the resulting surface is a topologica...
We present a new (1 + ε)-spanner for sets of n points in Rd . Our spanner has size O(n/εd−1 ) and maximum degree O(logd n). The main advantage of our spanner is that it can be...
Abstract. In wireless communication networks, optimal use of the directional antenna is very important. The directional antenna coverage (DAC) problem is to cover all clients with ...