Abstract. The classical Gibbs phenomenon for the Fourier sections (best L2trigonometric polynomial approximants) of a jump function asserts that, near the jump, the~e sections "overshoot" the function by an asymptotically constant factor g (the L2-Gibbs constant). In this paper we show that, for a class of one-jump discontinuous functions, a similar phenomenon holds for the trigonometric polyno...

Abstract. In this paper, we study the uniform hard capacitated k facility location problem (CkFLP) and knapsack median problem (CKM). Natural LP of both the problems have an unbounded integrality gap. Byrka et al. in [5] present an (O(1/ǫ)) for CkFLP violating cpapcities by a factor of (2 + ǫ). However, the proofs in [5] do not seem to work. In this paper, we first raise the issues in [5] and t...

We prove that every planar graph on n vertices is contained in a chordal graph with at most cn log n edges for some absolute constant c and this is best possible to within a constant factor.