The minimum spanning tree problem with conflict constraints and its variations

AbstractWe consider the minimum spanning tree problem with conflict constraints (MSTC). The problem is known to be strongly NP-hard and computing even a feasible solution is NP-hard. When the underlying graph is a cactus, we show that the feasibility problem is polynomially bounded whereas the optimization version is still NP-hard. When the conflict graph is a collection of disjoint cliques, (equivalently, when the conflict relation is transitive) we observe that MSTC can be solved in polynomial time. We also identify other special cases of MSTC that can be solved in polynomial time. Exploiting these polynomially solvable special cases we derive strong lower bounds. Also, various heuristic algorithms and feasibility tests are discussed along with preliminary experimental results. As a byproduct of this investigation, we show that if an ϵ-optimal solution to the maximum clique problem can be obtained in polynomial time, then a (3ϵ−1)-optimal solution to the maximum edge clique partitioning (Max-ECP) problem can be obtained in polynomial time. As a consequence, we have a polynomial time approximation algorithm for the Max-ECP with performance ratio O(n(loglogn)2log3n), improving the best previously known bound of O(n)

Observer-based Leader-following Consensus for Positive Multi-agent Systems Over Time-varying Graphs

This paper addresses the leader-following consensus problem for discrete-time positive multi-agent systems over time-varying graphs. We assume that the followers may have mutually different positive dynamics which can also be different from the leader. Compared with most existing positive consensus works for homogeneous multi-agent systems, the formulated problem is more general and challenging due to the interplay between the positivity requirement and high-order heterogeneous dynamics. To solve the problem, we present an extended version of existing observer-based design for positive multi-agent systems. By virtue of the common quadratic Lyapunov function technique, we show the followers will maintain their state variables in the positive orthant and finally achieve an output consensus specified by the leader. A numerical example is used to verify the efficacy of our algorithms

Video Manipulation Techniques for the Protection of Privacy in Remote Presence Systems

Systems that give control of a mobile robot to a remote user raise privacy concerns about what the remote user can see and do through the robot. We aim to preserve some of that privacy by manipulating the video data that the remote user sees. Through two user studies, we explore the effectiveness of different video manipulation techniques at providing different types of privacy. We simultaneously examine task performance in the presence of privacy protection. In the first study, participants were asked to watch a video captured by a robot exploring an office environment and to complete a series of observational tasks under differing video manipulation conditions. Our results show that using manipulations of the video stream can lead to fewer privacy violations for different privacy types. Through a second user study, it was demonstrated that these privacy-protecting techniques were effective without diminishing the task performance of the remote user.Comment: 14 pages, 8 figure