Circuit Imbalance Measures and Linear Programming

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This paper considers routing and link scheduling in a two-tier wireless backhaul network. The first tier consists of routers and the second tier consists of Radio Frequency (RF)-energy harvesting Internet of Things (IoT) devices that rely on routers for energy. Our aim is to derive the shortest Time Division Multiple Access (TDMA) link schedule that satisfies the traffic demand of routers and energy demand of IoT devices. We formulate a Linear Program (LP) to jointly derive a routing and link schedule solution. We also propose a heuristic link scheduler called Transmission Set Generation (TSG) to generate transmission sets and to derive the transmit power allocation of routers. In addition, we present a novel routing metric that considers RF-energy harvesting devices on a given path. TSG on average achieves 31.25% shorter schedules as compared to competing schemes. Lastly, our novel routing metric results in link schedules that are at most 24.75% longer than those computed by LP.

An Approximation Algorithm for the Two-Node-Connected Star Problem with Steiner Nodes

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Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates have been established for first order LP algorithms, despite the fact that the underlying formulations are not strongly convex. However, the convergence rate typically depends on the Hoffman constant of a large matrix that contains the constraint matrix, as well as the right hand side, cost, and capacity vectors. We introduce a first order approach for LP optimization with a convergence rate depending polynomially on the circuit imbalance measure, which is a geometric parameter of the constraint matrix, and depending logarithmically on the right hand side, capacity, and cost vectors. This provides much stronger convergence guarantees. For example, if the constraint matrix is totally unimodular, we obtain polynomial-time algorithms, whereas the convergence guarantees for approaches based on primal-dual formulations may have arbitrarily slow convergence rates for this class. Our approach is based on a fast gradient method due to Necoara, Nesterov, and Glineur (Math. Prog. 2019); this algorithm is called repeatedly in a framework that gradually fixes variables to the boundary. This technique is based on a new approximate version of Tardos's method, that was used to obtain a strongly polynomial algorithm for combinatorial LPs (Oper. Res. 1986).

The paper is devoted to Time Division Multiple Access Link Scheduling Protocols in wireless sensor networks for full duplex (two-way) communication, where each sensor is scheduled on an incident link as a transmitter and as a receiver in two different time slots. We formulate the full duplex link scheduling problem (FDLSP) as distance-2 edge coloring in bi-directed graphs and prove tighter lower and upper bounds for the FDLSP problem. We formulate the FDLSP problem as an integer linear program (ILP). Then, we present two I”-approximation distributed algorithms for growth bounded graphs (GBG), for modeling the sensor networks, and for general graphs, I” being the maximum node degree in the network. The first algorithm is a synchronous $\Delta$-approximation algorithm based on finding maximal independent sets. The second is an asynchronous I”-approximation depth first search (DFS) based algorithm. The maximal independent set based algorithm requires only O(I” log * n) communication rounds (where n is the number of processors in the network) in growth bounded graphs. For general graphs, the maximal independent set based algorithm requires O(I” 4 +I” 3 log * n) communication rounds, improving upon the previous best known algorithm with O(nI” 2 + n 2 m) communication rounds (where m is the number of links in the network). The asynchronous DFS based algorithm requires only O(n) communication rounds for both general and growth bounded graphs. The simulations show that the proposed algorithms assign on average equal or fewer number of time slots compared to the best known distributed algorithm while being significantly faster.

The ultra-high bandwidth available at millimeter (mmWave) and Terahertz (THz) frequencies can effectively realize short-range wireless access links in small cells enabling potential uses such as driver-less cars, ultra-high-definition infotainment services and data backhauling. In this context, in alternative to fiber-based and legacy wireless-based backhauling, vehicles can be used as digital mules to increase the data throughput of a region served by a software defined network (SDN) transmitting data to the Software Defined Base Station (SD-BS), equipped with only one mmWave/THz transceiver. In real applications, multiple vehicles may concurrently pass through the region and related data throughput depends on the relative distance with respect to the transceiver. For technological reasons, the SD-BS transceiver can be used by just one vehicle at each time instant (time-slot). Hence, an operational decision problem arises consisting in determining the assignment of the vehicles to the time-slots of the SD-BS maximizing the data throughput. The problem can be conceived as a variant of different combinatorial optimization problems like scheduling and assignment problems. An original mixed integer linear programming formulation of the problem is presented and tested on real-like instances generated from a case study.

Overlay multicasting providing live streaming services is a crucial service for the contemporary Internet. In this article, we focus on applying overlay multicasting for delivery of critical data that must be transmitted safely, intact, and with as little delay as possible; for example, financial data, software security patches, antivirus signature database updates, etc. To improve survivability of overlay multicasting, we propose using a dual homing approach; that is, each peer is connected to the overlay by two separate access links. We consider the following network failures: overlay link failure, uploading node failure, and Internet server provider (ISP) interconnection failure. The objective is to minimize the maximum delay in the network. The optimization problem is formulated in the form of an integer linear programming (ILP) model. We introduce a simulated annealing (SA) algorithm and a tabu search (TS) algorithm for the considered problem and compare them with optimal results provided by CPLEX solver. Our studies demonstrate that both SA and TS methods yield results close to optimal and provide better scalability compared to CPLEX, because they can solve much larger problem instances than CPLEX in reasonable time. Furthermore, our studies show that the additional survivability requirements do not have a substantial impact on the overlay multicasting system expressed as the maximum delay.

Due to growing demand for high definition music and video content, overlay multicasting providing live streaming services has been gaining popularity in the last years. In this paper, we focus on applying overlay multicasting for delivering of critical data that require to be transmitted safely, intact and with as little delay as possible. To improve survivability of the overlay multicasting, we propose to use dual homing approach, i.e., each peer is connected to the overlay by two separate access links. We consider the following network failures: overlay link failure, uploading node failure and ISP interconnection failure. The optimization problem is formulated in form of an Integer Linear Programming (ILP) model. We introduce a Simulated Annealing (SA) algorithm for the considered optimization problem and compare it with optimal results provided by CPLEX solver. We also introduce several distributed tree construction strategies and conduct simulation experiments to investigate problems of providing survivability to both static and dynamic types of the network. Our studies show that the additional survivability requirements do not have a substantial impact on the overlay multicasting system expressed as the streaming cost. Moreover, the introduced heuristic method yields results close to optimal and provides better scalability comparing to CPLEX, since it can solve in reasonable time much larger problem instances than CPLEX.

This paper presents a new distributed slot reservation frame-work for joint resource allocation and flow control in mmWave IAB networks. We derive the Dynamic Slot Reservation (DSR) algorithm from a novel approach to solve a minimum clearing time linear program in a completely distributed manner. The algorithm to solve this problem, the Static Slot Reservation (SSR) algorithm, is also a contribution of the paper. We compare the delay performance of the DSR algorithm with a well known optimal, centralized algorithm, the joint-MWM algorithm, for a realistic IAB network scenario of multi-hop flows. We show that flows that traverse several links have significantly lower delays under DSR than under the joint-MWM algorithm. This paper also provides an instantaneous rate control policy for IAB networks which changes flow rates based on the number of flows at each node in the network. The flow rates under this policy are the same as the steady-state flow rates achieved by the DSR algorithm. We prove that the proposed flow control policy provides stability for all flow arrival rate vectors that are achievable by any flow control policy. This paper provides distributed admission control policies to provide rate and/or latency guarantees to flows under dynamic scenarios with stochastic flow arrivals and changing access link rates.

Optimal capacity partitioning in peer-to-peer (p2p) file sharing system has been a topic of discussion in recent years by many research scholars. In Various network like Wi-Fi, WLAN, LTE, and WiMAX, the access link capacity division between uplink and downlink can be modified by the peers. Each peer is allocated a link capacity by the network which can be used for uplink and downlink. This available link capacity can be judiciously divided between uplink and downlink in such a way that peers requirement is fulfilled while keeping the uplink minimum. The sum of uplink and download capacity is constant for fixed unit of time. So uplink and downlink capacity of each peer has been represented in terms of a variable. This paper aims to minimize the value of the variable such that uplink is minimum as well as requirement of each peer is fulfilled. In P2P file sharing system, the download requirements of the terminals have been described by a constant constraint system with addition-min relation inequalities. A linear programming approach is developed to find the minimum value of variable which makes the uplink minimum with satisfying the peers' requirement.

The exponential growth in demand for mobile data requires significant increases in spatial reuse, motivating an evolution towards picocellular architectures with densely deployed base stations. Providing backhaul for such a network is a key challenge, because of the high access link rates, and the cost and difficulty of running optical fiber to base stations that might be opportunistically placed on lampposts and rooftops. Wireless backhaul using millimeter (mm) wave spectrum is therefore an attractive and flexible approach, given the plentiful availability of spectrum and the possibility of synthesizing highly directive, steerable links. In this paper, we formulate and investigate the problem of joint resource allocation and routing on such a mm wave backhaul network, providing a linear programming formulation that accounts for mutual interference across simultaneously active links. While the number of variables grows exponentially in network size, it is possible to prune the problem size so that it is manageable for moderately sized networks. Numerical results and design implications are briefly discussed.

Due to growing demand for high definition music and video content, Peer to Peer (P2P) multicasting providing live streaming services has been gaining popularity in the last years. In this paper, we focus on applying the P2P multicasting for delivering of critical data that require to be transmitted safely, intact and with as little delay as possible, e.g., financial data, software security patches, antivirus signature database updates etc. To improve survivability of the P2P multicasting, we propose to use dual homing approach, i.e., each peer is connected to the overlay by two separate access links. The optimization problem is formulated in the form of Integer Linear Programming (ILP). We introduce a Simulated Annealing (SA) algorithm for the considered optimization problem and compare it with optimal results provided by CPLEX solver. Our studies demonstrate that the SA method yields results close to optimal and provides better scalability comparing to CPLEX, since it can solve in reasonable time much larger problem instances than CPLEX.

Due to recent developments in cloud computing and constantly increasing demand for high definition music and video content, both overlay networks and multicasting providing live streaming services along with network survivability have been gaining more and more attention in the last years. In our paper, we focus on the problem of Capacity and Flow Assignment (CFA) in survivable overlay networks. We assume that the overlay network is deployed to provide multicasting of critical data that require to be transmitted safely and with minimum possible delay. We propose to use a dual homing approach, i.e., each peer is connected to the overlay by two separate access links, to improve survivability of the overlay multicasting. We consider the following network failures: streaming server failure, overlay link failure, uploading node failure and ISP interconnection failure. The optimization problem is formulated in the form of an Integer Linear Programming (ILP) model. Moreover, we introduce a heuristic algorithm (Simulated Annealing) for the given problem and compare it with optimal results achieved by the ILP modeling (CPLEX solver). Our studies demonstrate that the Simulated Annealing (SA) method yields results close to optimum and provides better scalability comparing to ILP modeling, since SA can solve in a reasonable time much larger problem instances than ILP modeling. Furthermore, our studies show that the additional survivability requirements do not have a substantial impact on the overlay multicasting system expressed as the maximum delay in case of the CFA problem.

Service Overlay Networks (SONs) allow virtual operators to create and deploy value-added Internet services with Quality of Service guarantees, while leaving the underlying network infrastructure unchanged. The deployment of a SON can be very expensive, and hence its planning requires careful decisions, including the overlay nodes’ placement and the capacity provisioning of the access links that connect the end-users to the SON infrastructure.In this work we first propose a novel Integer Linear Programming (ILP) model for the overlay network design problem which selects the optimal number and position of overlay nodes, the capacity reserved on each overlay link, as well as the optimal routing of the incoming traffic demands.Since such model can be solved to the optimum only for small network instances, we further propose an efficient and novel tabu search based heuristic for the planning of SONs that combines polynomial size and very large-scale neighborhoods. The very large-scale neighborhood of the solution given by tabu search is explored efficiently to obtain in a short time a new one that is both far from the current solution and cost-decreasing.We provide numerical results of the proposed heuristic on a set of realistic, large-size instances, including real ISP topologies, and discuss the effect of different parameters on the characteristics of the planned networks. Furthermore, we compare such results with the bound obtained solving our ILP model in small network scenarios. We show that in the considered network topologies the proposed heuristic performs very close to the optimum with a short computation time, thus providing a promising framework for the design of SONs.