The bistatic backscatter architecture, with its extended range, enables flexible deployment opportunities for devices. In this paper, we study the placement of power beacons (PBs) in networks to maximize guaranteed coverage distance (GCD), defined as from reader within which devices are able satisfy a given quality-of-service constraint. This work departs conventional energy source problems by ...

This paper presents an algorithm and its implementation for computing the approximate GCD (greatest common divisor) of multivariate polynomials whose coefficients may be inexact. The method and the companion software appears to be the first practical package with such capabilities. The most significant features of the algorithm are its robustness and accuracy as demonstrated in the results of c...

We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and prove that its bit-time complexity is still O(n) for two n-bit integers. However, our preliminar experiments show that it is very fast for small integers. A parallel version of this algorithm matches the best presently known time complexity, na...

Let E/k(T ) be an elliptic curve defined over a rational function field of characteristic zero. Fix a Weierstrass equation for E. For points R ∈ E(k(T )), write xR = AR/D2 R with relatively prime polynomials AR(T ), DR(T ) ∈ k[T ]. The sequence {DnR}n≥1 is called the elliptic divisibility sequence of R. Let P, Q ∈ E(k(T )) be independent points. We conjecture that deg ( gcd(DnP , DmQ) ) is boun...

We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF (2)-linear combination of Gold functions Tr(x i+1) is semi-bent over GF (2), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold fu...

We introduce an algorithm to interpolate sparse multivariate polynomials with integer coefficients. Our algorithm modifies Ben-Or and Tiwari’s deterministic algorithm for interpolating over rings of characteristic zero to work modulo p, a smooth prime of our choice. We present benchmarks comparing our algorithm to Zippel’s probabilistic sparse interpolation algorithm, demonstrating that our alg...

where z is an integer then gcd(a, b) = gcd(b, c). Indeed any divisor of a and b will divide c, and conversely any divisor of b and c will divide a. We can compute c by taking the remainder after dividing a by b, i.e. c is a mod b. (We will discuss the mod operation in greater details in the next section, but at this point, we only need the definition of c as the remainder of dividing a by b.) B...

In this paper, we propose and study an Asynchronous parallel Greedy Coordinate Descent (Asy-GCD) algorithm for minimizing a smooth function with bounded constraints. At each iteration, workers asynchronously conduct greedy coordinate descent updates on a block of variables. In the first part of the paper, we analyze the theoretical behavior of Asy-GCD and prove a linear convergence rate. In the...

This paper describes parallel matrix transpose algorithms on distributed memory concurrent processors. We assume that the matrix is distributed over a P Q processor template with a block scattered data distribution. P , Q, and the block size can be arbitrary, so the algorithms have wide applicability. The communication schemes of the algorithms are determined by the greatest common divisor (GCD...