A multi-link communication connectivity game under hostile interference

In this paper, we consider a communication connectivity problem involving a primary user (transmitter, for example, a Ground Control Station (GCS)) servicing a group of secondary users (receivers, for example, drones) under hostile interference. We formulate this multi-link communication connectivity problem, where the channels are affected by Rayleigh fading, as a zero-sum power resource allocation game between a transmitter and an adversary (jammer). The transmitter's objective is to maximize the probability of communication connectivity with all the receivers. It is proven that the problem has unique equilibrium in power allocation strategies, and the equilibrium is derived in closed form. Moreover, we reduce the problem of designing the equilibrium in power resource allocation strategies to the problem of finding a fixed point of a real-valued function. An algorithm based on the bisection method to find the fixed point (and so equilibrium strategies) is developed, and its convergence is proven.

Algorithm for Graph’s Connectivity Problem Based on DNA Origami

Based on DNA origami, an algorithm is proposed for Graph’s Connectivity problem via the self-assembly of DNA origami structures. The desired DNA origami structures can be constructed. These structures can encode the information of Graph’s vertices and edges, because these structures have sticky ends, so they can assemble to advanced structures representing the information of a graph via specific hybridization. Via strand displacement reaction and agarose gel electrophoresis, the vertices can be deleted and the graph’s connectivity can be tested one by one. This is a highly parallel method, and can reduce the complexity of Graph’s Connectivity problem greatly.

Robust Connectivity for Multiagent Systems using Mixed-Integer Programming

This work is concerned with the problem of planning trajectories for a group of mobile robots operating in a obstacle-filled environment. The objective of the robots is to cooperatively reach targets sets, avoiding collisions between themselves and with obstacles, while maintaining the robust connectivity of their communication network. Model predictive control with mixed-integer encoding is used to plan the trajectories in a centralized fashion. Two novel constraints are introduced to cope with the robustness connectivity problem. Simulations are provided to evaluate the proposal.

Time and space efficient quantum algorithms for detecting cycles and testing bipartiteness

We study space and time-efficient quantum algorithms for two graph problems – deciding whether an n-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for deciding both properties in O˜(n 3/2 ) time whilst using O(log n) classical and quantum bits of storage in the adjacency matrix model. We then present quantum algorithms for deciding the two properties in the adjacency array model, which run in time O˜(n √ dm) and also require O(log n) space, where dm is the maximum degree of any vertex in the input graph.