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In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations, where genomes allow a mix of linear and circular chromosomes to be present. First, we formulate an equivalent optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in a breakpoint graph. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than l can be reduced to the well-known degree-bounded k-set packing problem with k = 2l. Finally, a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by double-cut-and-join operations is devised, which achieves the approximation ratio for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved to

To boost the performance of wireless communication networks, unmanned aerial vehicles (UAVs) aided communications have drawn dramatically attention due to their flexibility in establishing the line of sight (LoS) communications. However, with the blockage in the complex urban environment, and due to the movement of UAVs and mobile users, the directional paths can be occasionally blocked by trees and high-rise buildings. Intelligent reflection surfaces (IRSs) that can reflect signals to generate virtual LoS paths are capable of providing stable communications and serving wider coverage. This is the first paper that exploits a three-dimensional geometry dynamic channel model in IRS-assisted UAV-enabled communication system. Moreover, we develop a novel deep learning based channel tracking algorithm consisting of two modules: channel preestimation and channel tracking. A deep neural network with off-line training is designed for denoising in the pre-estimation module. Moreover, for channel tracking, a stacked bi-directional long short term memory (Stacked Bi-LSTM) is developed based on a framework that can trace back historical time sequence together with bidirectional structure over multiple stacked layers. Simulations have shown that the proposed channel tracking algorithm requires fewer epochs to convergence compared to benchmark algorithms. It also demonstrates that the proposed algorithm is superior to different benchmarks with small pilot overheads and comparable computation complexity.

Abstract-In this letter, we propose a novel modularity-based dynamic clustering relying on modified Louvain method for UAVs aided mobile communications. Our aim is to save the transmit power of the mobile devices, by locating the UAVs vertically projected on the centroids of the user clusters. We further propose two types of operation for the modularitybased dynamic clustering, namely the recurring operation and the differential operation. We show that the proposed method requires substantially lower transmit power of the mobile devises and lower energy consumption of the UAVs than that required by the K-means based solution. We also show that the differential operation is more suitable for networks with lower proportion of moving users, since it consumes significantly less energy than that required by the recurring operation at the cost of requiring slightly higher transmit power of mobile devices. I. INTRODUCTIONRecently, unmanned aerial vehicles (UAVs) aided mobile communications has drawn great attentions, thanks to its capability in providing better line-of-sight (LoS) connections with adjustable flying positions. The use cases of the UAVs aided mobile communications mainly cover emergency-responding services for both public and military areas [1]. Recent studies have investigated various air-to-ground channel models [2], flying altitude versus coverage trade-offs [3], energy efficient UAV transmission schemes [4], etc. Indeed, it is highly important to save the transmit power of mobile devices so that to prolong their usage in emergency scenarios. One promising approach is to locate the UAVs closer to the mobile devices for establishing shorter radio links. To elaborate, [5] showed that the transmit power of mobile devices can be substantially reduced by adapting the UAVs' positions based on the mobile devices' locations.In UAVs aided mobile communications, each UAV serves a cluster of mobile devices, where the clustering is typically based on the de facto K-means criteria. However, it is known from network science that modularity is the most used and best measure of the quality of clustering performance. Indeed, it has been widely studied in sociology, biology and computer science in terms of community detection [6]. Hence, we propose a novel modularity-based dynamic clustering for energy efficient UAVs aided mobile communications, relying on modified Louvain method in both recurring and differential operation to construct clusters. Specifically, after forming dynamic clusters, the UAVs are relocated to the positions vertically projected on the centroids of clusters.

By employing powerful edge servers for data processing, mobile edge computing (MEC) has been recognized as a promising technology to support emerging computation-intensive applications. Besides, non-orthogonal multiple access (NOMA)aided MEC system can further enhance the spectral-efficiency with massive tasks offloading. However, with more dynamic devices brought online and the uncontrollable stochastic channel environment, it is even desirable to deploy appealing technique, i.e., intelligent reflecting surfaces (IRS), in the MEC system to flexibly tune the communication environment and improve the system energy efficiency. In this paper, we investigate the joint offloading, communication and computation resource allocation for the IRS-assisted NOMA MEC system. We first formulate a mixed integer energy efficiency maximization problem with system queue stability constraint. We then propose the Lyapunovfunction-based Mixed Integer Deep Deterministic Policy Gradient (LMIDDPG) algorithm which is based on the centralized reinforcement learning (RL) framework. To be specific, we design the mixed integer action space mapping which contains both continuous mapping and integer mapping. Moreover, the award function is defined as the upper-bound of the Lyapunov driftplus-penalty function. To enable end devices (EDs) to choose actions independently at the execution stage, we further propose the Heterogeneous Multi-agent LMIDDPG (HMA-LMIDDPG) algorithm based on distributed RL framework with homogeneous EDs and heterogeneous base station (BS) as heterogeneous multiagent. Numerical results show that our proposed algorithms can achieve superior energy efficiency performance to the benchmark algorithms while maintaining the queue stability. Specially, the distributed structure HMA-LMIDDPG can acquire more energy efficiency gain than the centralized structure LMIDDPG.