Linial’s seminal result shows that any deterministic distributed algorithm that finds a 3-colouring of an n-cycle requires at least log∗(n)/2 − 1 communication rounds. We give a new simpler proof of this theorem.

We address two problems. In the first, we refine the analysis of a lower bound construction of a point set having many non-crossing spanning trees. We also give more precise upper bounds on the maximum number of non-crossing spanning trees, perfect matchings and simple polygons of a planar point set. In the second, we give an improved lower bound construction for the d-interval problem. 1 Non-c...

Needless to say, sorting, especially sorting by comparisons, has been a classical problem in computer science. Despite its enormous importance, the complexity, in terms of the number of comparisons needed, is simple to analyze. Straightforward information theoretical argument gives the tight lower bound of log2(n!), which is achieved by several simple sorting algorithms, for example, Insertion ...

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...

We show that an improvement to the best known quantum lower bound for Graph-Collision problem implies an improvement to the best known lower bound for Triangle problem in the quantum query complexity model. In Graph-Collision we are given free access to a graph (V,E) and access to a function f : V → {0, 1} as a black box. We are asked to determine if there exist (u, v) ∈ E, such that f(u) = f(v...

A (d − 1)-dimensional simplicial complex is called balanced if its underlying graph admits a proper d-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs). Specifically, we prove the balanced analog of the celebrated Lower Bound Theorem for normal pseudomanifolds and characterize the case of equality; we introduce and ch...

 Abstract : A visual cryptography scheme based on a given graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper a maximal independent sets of the graph G was ...