Improved Approximation Algorithms for Relay Placement

In the relay placement problem the input is a set of sensors and a number $r \ge 1$, the communication range of a relay. In the one-tier version of the problem the objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance $r$ if both vertices are relays and within distance 1 otherwise. The two-tier version adds the restrictions that the path must go through relays, and not through sensors. We present a 3.11-approximation algorithm for the one-tier version and a PTAS for the two-tier version. We also show that the one-tier version admits no PTAS, assuming P $\ne$ NP.Comment: 1+29 pages, 12 figure

Optimal Placement Algorithms for Virtual Machines

Cloud computing provides a computing platform for the users to meet their demands in an efficient, cost-effective way. Virtualization technologies are used in the clouds to aid the efficient usage of hardware. Virtual machines (VMs) are utilized to satisfy the user needs and are placed on physical machines (PMs) of the cloud for effective usage of hardware resources and electricity in the cloud. Optimizing the number of PMs used helps in cutting down the power consumption by a substantial amount. In this paper, we present an optimal technique to map virtual machines to physical machines (nodes) such that the number of required nodes is minimized. We provide two approaches based on linear programming and quadratic programming techniques that significantly improve over the existing theoretical bounds and efficiently solve the problem of virtual machine (VM) placement in data centers

Optimal Data Placement on Networks With Constant Number of Clients

We introduce optimal algorithms for the problems of data placement (DP) and page placement (PP) in networks with a constant number of clients each of which has limited storage availability and issues requests for data objects. The objective for both problems is to efficiently utilize each client's storage (deciding where to place replicas of objects) so that the total incurred access and installation cost over all clients is minimized. In the PP problem an extra constraint on the maximum number of clients served by a single client must be satisfied. Our algorithms solve both problems optimally when all objects have uniform lengths. When objects lengths are non-uniform we also find the optimal solution, albeit a small, asymptotically tight violation of each client's storage size by $\epsilon$lmax where lmax is the maximum length of the objects and $\epsilon$ some arbitrarily small positive constant. We make no assumption on the underlying topology of the network (metric, ultrametric etc.), thus obtaining the first non-trivial results for non-metric data placement problems

Cache Placement in Fog-RANs: From Centralized to Distributed Algorithms

To deal with the rapid growth of high-speed and/or ultra-low latency data traffic for massive mobile users, fog radio access networks (Fog-RANs) have emerged as a promising architecture for next-generation wireless networks. In Fog-RANs, the edge nodes and user terminals possess storage, computation and communication functionalities to various degrees, which provides high flexibility for network operation, i.e., from fully centralized to fully distributed operation. In this paper, we study the cache placement problem in Fog-RANs, by taking into account flexible physical-layer transmission schemes and diverse content preferences of different users. We develop both centralized and distributed transmission aware cache placement strategies to minimize users' average download delay subject to the storage capacity constraints. In the centralized mode, the cache placement problem is transformed into a matroid constrained submodular maximization problem, and an approximation algorithm is proposed to find a solution within a constant factor to the optimum. In the distributed mode, a belief propagation based distributed algorithm is proposed to provide a suboptimal solution, with iterative updates at each BS based on locally collected information. Simulation results show that by exploiting caching and cooperation gains, the proposed transmission aware caching algorithms can greatly reduce the users' average download delay.Comment: 13 pages, 10 figure

A new layout optimization technique for interferometric arrays, applied to the MWA

Antenna layout is an important design consideration for radio interferometers because it determines the quality of the snapshot point spread function (PSF, or array beam). This is particularly true for experiments targeting the 21 cm Epoch of Reionization signal as the quality of the foreground subtraction depends directly on the spatial dynamic range and thus the smoothness of the baseline distribution. Nearly all sites have constraints on where antennas can be placed---even at the remote Australian location of the MWA (Murchison Widefield Array) there are rock outcrops, flood zones, heritages areas, emergency runways and trees. These exclusion areas can introduce spatial structure into the baseline distribution that enhance the PSF sidelobes and reduce the angular dynamic range. In this paper we present a new method of constrained antenna placement that reduces the spatial structure in the baseline distribution. This method not only outperforms random placement algorithms that avoid exclusion zones, but surprisingly outperforms random placement algorithms without constraints to provide what we believe are the smoothest constrained baseline distributions developed to date. We use our new algorithm to determine antenna placements for the originally planned MWA, and present the antenna locations, baseline distribution, and snapshot PSF for this array choice.Comment: 12 pages, 6 figures, 1 table. Accepted for publication in MNRA

Feature placement algorithms for high-variability applications in cloud environments

While the use of cloud computing is on the rise, many obstacles to its adoption remain. One of the weaknesses of current cloud offerings is the difficulty of developing highly customizable applications while retaining the increased scalability and lower cost offered by the multi-tenant nature of cloud applications. In this paper we describe a Software Product Line Engineering (SPLE) approach to the modelling and deployment of customizable Software as a Service (SaaS) applications. Afterwards we define a formal feature placement problem to manage these applications, and compare several heuristic approaches to solve the problem. The scalability and performance of the algorithms is investigated in detail. Our experiments show that the heuristics scale and perform well for systems with a reasonable load