A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was a longstanding open problem, and recently a polynomial-time algorithm has been given [G. B. Mertzios, The Recognition of Simple-Triangle Graphs and of Linea...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Abstract Let $X \subset \mathbf {P}^n$ be an irreducible hypersurface of degree $d\geq 3$ with only isolated semi-weighted homogeneous singularities, such that $\exp (\frac {2\pi i}{k})$ is a zero its Alexander polynomial. Then we show the equianalytic deformation space $X$ not $T$-smooth except for finite list triples $(n,d,k)$. This result captures very classical examples by B. Segre families...

Phylogenetic trees canonically arise as embeddings of phylogenetic networks. We recently showed that the problem deciding if two networks embed same sets is computationally hard, \blue{in particular, we it to be $\Pi^P_2$-complete}. In this paper, establish a polynomial-time algorithm for decision initial consists normal network and tree-child network. The running time quadratic in size leaf se...

This paper presents a polynomial connectionist network called ridge polynomial network (RPN) that can uniformly approximate any continuous function on a compact set in multidimensional input space R (d), with arbitrary degree of accuracy. This network provides a more efficient and regular architecture compared to ordinary higher-order feedforward networks while maintaining their fast learning p...

The expected number of zeros a random real polynomial degree $N$ asymptotically equals $\frac{2}{\pi}\log N$. On the other hand, average fraction trigonometric increasing converges to not $0$ but $1/\sqrt 3$. An roots system polynomials in several variables is equal mixed volume some ellipsoids depending on degrees polynomials. Comparing this formula with Theorem BKK we prove that phenomenon no...

We study the scheduling situation where n tasks, subjected to release dates and due dates, have to be scheduled on m parallel processors. We show that, when tasks have unit processing times and either require 1 or m processors simultaneously, the minimum maximal tardiness can be computed in polynomial time. The complexity status of this “tall/small” task scheduling problem P|ri, pi = 1, sizei ∈...

We study the problem of minimizing the broadcast time for a set of processors in a cluster, where processor pi has transmission time ti, which is the time taken to send a message to any other processor in the cluster. Previously, it was shown that the Fastest Node First method (FNF) gives a 1.5 approximate solution. In this paper we show that there is a polynomial time approximation scheme for ...

In this paper, we give an abstraction of multi-secret sharing schemes based on lagrange interpolating polynomial that is accessible to a fully mechanized analysis. The abstraction is formalized within the applied pi-calculus using an equational theory that abstractly characterizes the cryptographic semantics of secret share. Based on that, we verify the threshold certificate protocol in a conve...

We study the factoring with known bits problem, where we are given a composite integer N = p1p2 . . . pr and oracle access to the bits of the prime factors pi, i = 1, . . . , r. Our goal is to find the full factorization of N in polynomial time with a minimal number of calls to the oracle. We present a rigorous algorithm that efficiently factors N given (1− 1 r Hr) log N bits, where Hr denotes ...