We study the spherical slice transform [Formula: see text] which assigns to a function f on unit sphere S n in integrals of over cross-sections by k-dimensional affine planes passing through north pole (0,…, 0, 1). These transforms are known when k = n. consider all 2 ≤ and obtain an explicit formula connecting with classical (k − 1)-plane Radon–John text]. Using this connection, facts for R k−...

A family F ⊂ 2[n] is called intersecting, if any two of its sets intersect. Given an intersecting family, its diversity is the number of sets not passing through the most popular element of the ground set. Frankl made the following conjecture: for n > 3k > 0 any intersecting family F ⊂ ([n] k ) has diversity at most ( n−3 k−2 ) . This is tight for the following “two out of three” family: {F ∈ (...

In this paper, we address the problem of k-out-of-` exclusion, a generalization of the mutual exclusion problem, in which there are ` units of a shared resource, and any process can request up to k units (1 ≤ k ≤ `). A protocol is self-stabilizing if, starting from an arbitrary configuration, be it initial state or after a corrupted state, the protocol can start behaving normally within a finit...

In this paper we present a parallel formulation of a multilevel k-way graph partitioning algorithm, that is particularly suited for high latency message-passing libraries. The multilevel k-way partitioning algorithm reduces the size of the graph by collapsing vertices and edges (coarsening phase), finds a k-way partitioning of the smaller graph, and then it constructs a k-way partitioning for t...

A graph G is called k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G through these vertices in the order. A vertex set S is called cyclable in G if there exists a cycle passing through all vertices of S. We will define “set-orderedness” which is a natural generalization of k-orderedness and cyclability. We also give a degree sum condition for graphs to satisf...

In this paper, we propose the partition approach and define several new classes of partitioned failure detectors weaker than existing failure detectors for the k-set agreement problem in both the shared-memory model and the message-passing model. In the shared-memory model with n + 1 processes, for any 2 ≤ k ≤ n, we first propose a partitioned failure detector ΠΩk that solves k-set agreement wi...

Table of contents §9.0. Foreword. §9.1. My more general auxiliary functions in the case k = 1, 2, 3. §9.2. Some relations for the functions, considered in §9.1 in the case l = 0. §9.3. Passing to the system of difference equations for the functions, considered in §9.2. §9.4. Passing from (τ, μ), to (α, ν) in the case l = 0. §9.0. Foreword. Let |z| ≥ 1,−3π/2 < arg(z) ≤ π/2, log(z) = ln(|z|) + i ...

Consider a message-passing system of n processors, in which each processor holds one piece of data initially. The goal is to compute an associative and commutative reduction function on the n pieces of data and to make the result known to all the n processors. This operation is frequently used in many message-passing systems and is typically referred to as global combine, census computation, or...

This paper shows that all shared atomic object types that can solve consensus among k > 1 processes have the same weakest failure detector in a message passing system with process crash failures. In such a system, object types such as test-and-set, fetch-and-add, and queue, known to have weak synchronization power in a shared memory system are thus, in a precise sense, equivalent to universal t...