A Hybrid Quantum Algorithm for Load Flow

We study a hybrid quantum algorithm for solving the AC load flow problem. The algorithm uses a quantum algorithm to compute the direction in the Newton-Raphson method. This hybrid approach offers scalability and improved convergence rates in theory

On a class of covering problems with variable capacities in wireless networks

We consider the problem of allocating clients to base stations in wireless networks. Two design decisions are the location of the base stations, and the power levels of the base stations. We model the interference, due to the increased power usage resulting in greater serving radius, as capacities that are non-increasing with respect to the covering radius. Clients have demands that are not necessarily uniform and the capacity of a facility limits the total demand that can be served by the facility. We consider three models. In the first model, the location of the base stations and the clients are fixed, and the problem is to determine the serving radius for each base station so as to serve a set of clients with maximum total profit subject to the capacity constraints of the base stations. In the second model, each client has an associated demand in addition to its profit. A fixed number of facilities have to be opened from a candidate set of locations. The goal is to serve clients so as to maximize the profit subject to the capacity constraints. In the third model, the location and the serving radius of the base stations are to be determined. There are costs associated with opening the base stations, and the goal is to open a set of base stations of minimum total cost so as to serve the entire demand subject to the capacity constraints at the base stations. We show that for the first model the problem is NP-complete even when there are only two choices for the serving radius, and the capacities are 1, 2. For the second model, we give a 1/2 approximation algorithm. For the third model, we give a column generation procedure for solving the standard linear programming model, and a randomized rounding procedure. We establish the efficacy of the column generation based rounding scheme on randomly generated instances

VERY SHORT COURSE ON LP

Given a matrix A ∈ R m×n and vectors b ∈ R m and c ∈ R n, a linear program (LP) is an optimisation problem of the form min x {c T x: Ax ≥ b}. (LP1) x is the solution vector, the value c T x is the cost associated with solution x, A is the constraint matrix, and b is called sometimes right hand side vector. An integer programming (IP) problem is a linear program in which the solution vector must be integral, i.e. all components must be integers. min x {c T x: Ax ≥ b, x ∈ Z n} (IP1) While (LP1) belongs to the complexity class P, (IP1) is an NP-hard problem. The most frequently used algorithm to solve LP problems, the simplex method, is efficient in practice but has an exponential worst case running time. A detailed discussion and a list of useful pointers in the literature regarding the complexity of LP and IP problems can be found in the book of Schrijver [72]. This section gives a brie

Information Processing Letters 79 (2001) 215–221 On computing the optimal bridge between two convex polygons

Given two convex polygons P and Q we want to find a line segment (a bridge) that connects P and Q so that the maximum distance from a point inside P across the bridge to a point inside Q is minimized. We propose a linear-time algorithm to solv

Quantum Bitcoin Mining

This paper studies the effect of quantum computers on Bitcoin mining. The shift in computational paradigm towards quantum computation allows the entire search space of the golden nonce to be queried at once by exploiting quantum superpositions and entanglement. Using Grover’s algorithm, a solution can be extracted in time O(2256/t), where t is the target value for the nonce. This is better using a square root over the classical search algorithm that requires O(2256/t) tries. If sufficiently large quantum computers are available for the public, mining activity in the classical sense becomes obsolete, as quantum computers always win. Without considering quantum noise, the size of the quantum computer needs to be ≈104 qubits

QoS and Data Relaying for Wireless Sensor Networks

In this paper we study the effects of data relaying in wireless sensor networks (WS-Nets) under QoS constraints with two different strategies. In the first, data packets originating from the same source are sent to the base station possibly along several different paths, while in the second, exactly one path is used for this purpose. The two strategies correspond to splitting and not splitting relaying traffic respectively. We model a sensor network architecture based on a three-tier hierarchy of nodes which generalizes to a two-tier WSNet with multiple sinks. Our results apply therefore to both types of networks. Based on the assumptions in our model, we describe several methods for computing relaying paths that are optimal with respect to energy consumption and satisfy QoS requirements expressed by the delay with which data are delivered to the base station(s). We then use our algorithms to perform an empirical analysis that quantifies the performance gains and losses of the splittable and unsplittable traffic allocation strategies for wireless sensor networks with delayconstrained traffic. Our experiments show that splitting traffic does not provide a significant advantage in energy consumption, but can afford strategies for relaying data with a lower delay penalty when using a model based on soft-delay constraints. Key words: Sensor networks, data relaying, delay constraints.