We present a ck 2k approximation algorithm for the Max k-CSP problem (where c > 0.44 is an absolute constant). This result improves the previously best known algorithm by Hast, which has an approximation guarantee of Ω( k 2k log k ). Our approximation guarantee matches the upper bound of Samorodnitsky and Trevisan up to a constant factor (their result assumes the Unique Games Conjecture).

Greedy routing has drawn a lot of attention in research community. To our best knowledge, stretch factor has not been studied for greedy routing algorithms. In this paper, we propose a new greedy routing algorithm and take the initiative to evaluate its stretch factor. Our algorithm generalizes the algorithm presented in [1]. It embeds an n-vertex connected graph G(V,E) in a semi-metric space. ...

Let X be a random variable distributed according to the binomial distribution with parameters n and p . It is shown that P ( > E ) ⩾ 1 / 4 if c , where ≔ ln 3 best possible constant factor.

Let S2 be the 2-dimensional unit sphere and let Jα denote the nonlinear functional on the Sobolev space H1,2(S2) defined by Jα(u) = α 4 ∫

Given a multi-variant polynomial inequality with a parameter, how to find the best possible value of this parameter that satisfies the inequality? For instance, find the greatest number k that satisfies a+b+c+k(ab+bc+ca)−(k+1)(ab+bc+ca) ≥ 0 for all nonnegative real numbers a, b, c. Analogues problems often appeared in studies of inequalities and were dealt with by various methods. In this paper...

When the space L log+L is given the Hardy-Littlewood norm the best constant in the corresponding version of Zygmund's conjugate function inequality is shown to be r2 3~2 + 5-2 7-2 + • ■ ■ K = I-2 + 3"2 + 5"2 + 7" This complements the recent result of Burgess Davis that the best constant in Kolmogorov's inequality is K"1. The symbol K will be used throughout for the constant p2 _ 3-2 + 5-2 _ 7-2...

The goal of the paper is to initiate research towards a general, Blow-up Lemma type embedding statement for pseudo-random graphs with sublinear degrees. In particular, we show that if the second eigenvalue λ of a d-regular graph G on 3n vertices is at most cd/n logn, for some sufficiently small constant c> 0, then G contains a triangle factor. We also show that a fractional triangle factor alre...

We prove an optimal Hardy inequality for the fractional Laplacian on the half-space. 1. Main result and discussion Let 0 < α < 2 and d = 1, 2, . . .. The purpose of this note is to prove the following Hardy-type inequality in the half-space D = {x = (x1, . . . , xd) ∈ R : xd > 0}. Theorem 1. For every u ∈ Cc(D), (1) 1 2 ∫