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In this paper, we study algorithms for special cases of energy games, a class of turn-based games on graphs that show up in the quantitative analysis of reactive systems. In an energy game, the vertices of a weighted directed graph belong either to Alice or to Bob. A token is moved to a next vertex by the player controlling its current location, and its energy is changed by the weight of the edge. Given a fixed starting vertex and initial energy, Alice wins the game if the energy of the token remains nonnegative at every moment. If the energy goes below zero at some point, then Bob wins. The problem of determining the winner in an energy game lies in $\mathsf{NP} \cap \mathsf{coNP}$. It is a long standing open problem whether a polynomial time algorithm for this problem exists. We devise new algorithms for three special cases of the problem. The first two results focus on the single-player version, where either Alice or Bob controls the whole game graph. We develop an $\tilde{O}(n^\omega W^\omega)$ time algorithm for a game graph controlled by Alice, by providing a reduction to the All-Pairs Nonnegative Prefix Paths problem (APNP), where $W$ is the maximum weight and $\omega$ is the best exponent for matrix multiplication. Thus we study the APNP problem separately, for which we develop an $\tilde{O}(n^\omega W^\omega)$ time algorithm. For both problems, we improve over the state of the art of $\tilde O(mn)$ for small $W$. For the APNP problem, we also provide a conditional lower bound, which states that there is no $O(n^{3-\epsilon})$ time algorithm for any $\epsilon > 0$, unless the APSP Hypothesis fails. For a game graph controlled by Bob, we obtain a near-linear time algorithm. Regarding our third result, we present a variant of the value iteration algorithm, and we prove that it gives an $O(mn)$ time algorithm for game graphs without negative cycles.

Terahertz communication networks and intelligent reflecting surfaces exhibit significant potential in advancing wireless networks, particularly within the domain of aerial-based multi-access edge computing systems. These technologies enable efficient offloading of computational tasks from user electronic devices to Unmanned Aerial Vehicles or local execution. For the generation of high-quality task-offloading allocations, conventional numerical optimization methods often struggle to solve challenging combinatorial optimization problems within the limited channel coherence time, thereby failing to respond quickly to dynamic changes in system conditions. To address this challenge, we propose a deep learning-based optimization framework called Iterative Order-Preserving policy Optimization (IOPO), which enables the generation of energy-efficient task-offloading decisions within milliseconds. Unlike exhaustive search methods, IOPO provides continuous updates to the offloading decisions without resorting to exhaustive search, resulting in accelerated convergence and reduced computational complexity, particularly when dealing with complex problems characterized by extensive solution spaces. Experimental results demonstrate that the proposed framework can generate energy-efficient task-offloading decisions within a very short time period, outperforming other benchmark methods.

This paper investigates the ultra reliable and low latency communication (URLLC) performance of the IRS-aided MIMO system. The upper and lower bounds of the optimal average error probability (OAEP) for the coding rate within 1/sqrt(Mn) of the capacity are derived, where n and M represent the blocklength and the number of transmit antennas, respectively. To achieve this goal, a new central limit theorem (CLT) for the mutual information density over the IRS-aided MIMO system is derived in the asymptotic regime where the block-length, the IRS size, and number of the antennas go to infinity with the same pace. The CLT is then utilized to derive the closed-form upper and lower bounds for the OAEP. Based on the analysis result, a gradient-based algorithm is proposed to minimize the lower bound of the OAEP by optimizing the phase shift of the IRS. Simulation results validate the fitness of the CLT and the effectiveness of the proposed algorithm in optimizing the theoretical bound, as well as the performance of practical LDPC code.

With the fast development of reconfigurable intelligent surface (RIS), the network topology becomes more complex and varied, which makes the network design and analysis extremely challenging. Most of the current works adopt the binary system stochastic geometric, missing the coupling relationships between the direct and reflected paths caused by RISs. In this paper, we first define the typical triangle which consists of a base station (BS), a RIS and a user equipment (UE) as the basic ternary network unit in a RIS-assisted ultra-dense network (UDN). In addition, we extend the Campbell's theorem to the ternary system and present the ternary probability generating functional (PGFL) of the stochastic geometry. Based on the ternary stochastic geometry theory, we derive and analyze the coverage probability, area spectral efficiency (ASE), area energy efficiency (AEE) and energy coverage efficiency (ECE) of the RIS-assisted UDN system. Simulation results show that the RISs can improve the system performances, especially for the UE who has a high signal to interference plus noise ratio (SINR), as if the introduced RIS brings in Matthew effect. This phenomenon of RIS is appealing for guiding the design of complex networks.

In this paper, we address two crucial challenges in the design of cell-free (CF) systems: degradation in the performance of CF systems by imperfect channel state information at the transmitter (CSIT) and high computational/signaling loads arising from the increasing number of distributed antennas and parameters to be exchanged. To mitigate the effects of imperfect CSIT, we employ rate-splitting (RS) multiple-access, which separates the messages into common and private streams. Unlike prior works, we present a clustered CF multi-user multiple-antenna framework with RS, which groups the transmit antennas in several clusters to reduce the computational and signaling loads. The proposed RS-CF system employs one common stream per cluster to exploit the network diversity. Furthermore, we propose new cluster-based linear precoders for this framework. We then devise a power allocation strategy for the common and private streams within clusters and derive closed-form expressions for the sum-rate performance of the proposed cluster-based RS-CF system. Numerical results show that the proposed clustered RS-CF system and algorithms outperform existing approaches. % in terms of the sum-rate.

Edge computing is projected to become the dominant form of cloud computing in the future because of the significant advantages it brings to both users (less latency, higher throughput) and telecom operators (less Internet traffic, more local management). However, to fully unlock its potential at scale, system designers and automated optimization systems alike will have to monitor closely the dynamics of both processing and communication facilities. Especially the latter is often neglected in current systems since network performance in cloud computing plays only a minor role. In this paper, we propose the architecture of MECPerf, which is a solution to collect network measurements in a live edge computing domain, to be collected for offline provisioning analysis and simulations, or to be provided in real-time for on-line system optimization. MECPerf has been validated in a realistic testbed funded by the European Commission (Fed4Fire+), and we describe here a summary of the results, which are fully available as open data and through a Python library to expedite their utilization. This is demonstrated via a use case involving the optimization of a system parameter for migrating clients in a federated edge computing system adopting the GSMA platform operator concept.

Karppa & Kaski (2019) proposed a novel type of ``broken" or ``opportunistic" multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks. For instance, their algorithm can compute Boolean matrix multiplication in $O(n^{\log_2(6+6/7)} \log n) = O(n^{2.778})$ time. While faster matrix multiplication algorithms exist asymptotically, in practice most such algorithms are infeasible for practical problems. In this note, we describe an alternate way to use the broken matrix multiplication algorithm to approximately compute matrix multiplication, either for real-valued matrices or Boolean matrices. In brief, instead of running multiple iterations of the broken algorithm on the original input matrix, we form a new larger matrix by sampling and run a single iteration of the broken algorithm. Asymptotically, the resulting algorithm has runtime $O(n^{\frac{3 \log6}{\log7}} \log n) \leq O(n^{2.763})$, a slight improvement of Karppa-Kaski's algorithm. Since the goal is to obtain new practical matrix-multiplication algorithms, these asymptotic runtime bounds are not directly useful. We estimate the runtime for our algorithm for some sample problems which are at the upper limits of practical algorithms; unfortunately, for these parameters, the new algorithm does not appear to be beneficial.

This paper investigates the utilization of simultaneously transmitting and reflecting RIS (STAR-RIS) in supporting joint physical layer security (PLS) and covert communications (CCs) in a multi-antenna millimeter wave (mmWave) system, where the base station (BS) communicates with both covert and security users while defeating eavesdropping by wardens with the help of a STAR-RIS. Specifically, analytical derivations are performed to obtain the closed-form expression of warden's minimum detection error probability (DEP). Furthermore, the asymptotic result of the minimum DEP and the lower bound of the secure rates are derived, considering the practical assumption that BS only knows the statistical channel state information (CSI) between STAR-RIS and the wardens. Subsequently, an optimization problem is formulated with the aim of maximizing the average sum of the covert rate and the minimum secure rate while ensuring the covert requirement and quality of service (QoS) for legal users by jointly optimizing the active and passive beamformers. Due to the strong coupling among variables, an iterative algorithm based on the alternating strategy and the semi-definite relaxation (SDR) method is proposed to solve the non-convex optimization problem. Simulation results indicate that the performance of the proposed STAR-RIS-assisted scheme greatly surpasses that of the conventional RIS scheme, which validates the superiority of STAR-RIS in simultaneously implementing PLS and CCs.

In this paper, we analyze the performance of a reconfigurable intelligent surface (RIS)-assisted multi-hop transmission by employing multiple RIS units to enable favorable communication for a mixed free-space optical (FSO) and radio-frequency (RF) system. We consider a single-element RIS since it is hard to realize phase compensation for multiple-element RIS in the multi-hop scenario. We develop statistical results for the product of the signal-to-noise ratio (SNR) of the cascaded multiple RIS-equipped wireless communication. We use decode-and-forward (DF) and fixed-gain (FG) relaying protocols to mix multi-RIS transmissions over RF and FSO technologies and derive probability density and distribution functions for both the relaying schemes by considering independent and nonidentical double generalized gamma (dGG) distribution models for RF transmissions with line-of-sight (LOS) and inverse-Gamma shadowing effect and atmospheric turbulence for FSO system combined with pointing errors. We analyze the outage probability, and average bit-error rate (BER) performance of the considered system. We also present an asymptotic analysis of the outage probability using gamma functions to provide insight into the considered system in the high SNR regime. We use computer simulations to validate the derived analytical expressions and demonstrate the performance for different system parameters on the RIS-assisted multi-hop transmissions for a vehicular communication system.

Driven by the visions of Internet of Things and 5G communications, the edge computing systems integrate computing, storage and network resources at the edge of the network to provide computing infrastructure, enabling developers to quickly develop and deploy edge applications. Nowadays the edge computing systems have received widespread attention in both industry and academia. To explore new research opportunities and assist users in selecting suitable edge computing systems for specific applications, this survey paper provides a comprehensive overview of the existing edge computing systems and introduces representative projects. A comparison of open source tools is presented according to their applicability. Finally, we highlight energy efficiency and deep learning optimization of edge computing systems. Open issues for analyzing and designing an edge computing system are also studied in this survey.