This paper presents a randomized parallel algorithm for the Maximal Independent Set problem. Our algorithm uses a BSP-like computer with p processors and requires that n+m p = (p) for a graph with n vertices and m edges. Under this scalability assumption, and after a prepro-cessing phase, it computes a maximal independent set after O(log p) communication rounds, with high probability, each roun...

The main combinatorial result in this article is a classification of bar partitions of n which are of maximal p-bar weight for all odd primes p ≤ n. As a consequence, we show that apart from very few exceptions any irreducible spin character of the double covers of the symmetric and alternating groups vanishes on some element of odd prime order.

In a graph or a network G = (V,E), a set S ⊆ V is a 2-packing if ∀i ∈ V : |N [i] ∩ S| ≤ 1, where N [i] denotes the closed neighborhood of node i. A 2-packing is maximal if no proper superset of S is a 2-packing. This paper presents a safely converging self-stabilizing algorithm for maximal 2-packing problem. Under a synchronous daemon, it quickly converges to a 2packing (a safe state, not neces...

In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are ...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

We investigate the behaviour of linear cellular automata with state space ZN and only finitely many states. After some general comments about linear cellular automata over ZN , the general case is reduced to that of N being the power of a prime. For a prime power modulus, it is proved under fairly general conditions that the period length for “most” orbits increase by a factor of p when the mod...

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...

Let m(n, k) be the maximum number of prime implicants that any k-CNF on n variables can have. We show that 3 n 3 ≤ m(n, 2) ≤ (1 + o(1))3n3 .

An algorithm due to Bengalloun that continuously enumerates the primes is adapted to give the rst prime number sieve that is simultaneously sublinear, additive, and smoothly incremental: { it employs only (n= log log n) additions of numbers of size O(n) to enumerate the primes up to n, equalling the performance of the fastest known algorithms for xed n; { the transition from n to n + 1 takes on...