Distributed computing frameworks such as MapReduce are often used to process large computational jobs. They operate by partitioning each job into smaller tasks executed on different servers. The servers also need to exchange intermediate values to complete the computation. Experimental evidence suggests that this so-called Shuffle phase can be a significant part of the overall execution time for several classes of jobs. Prior work has demonstrated a natural tradeoff between computation and communication whereby running redundant copies of jobs can reduce the Shuffle traffic load, thereby leading to reduced overall execution times. For a single job, the main drawback of this approach is that it requires the original job to be split into a number of files that grows exponentially in the system parameters. When extended to multiple jobs (with specific function types), these techniques suffer from a limitation of a similar flavor, i.e., they require an exponentially large number of jobs to be executed. In practical scenarios, these requirements can significantly reduce the promised gains of the method. In this work, we show that a class of combinatorial structures called resolvable designs can be used to develop efficient coded distributed computing schemes for both the single and multiple job scenarios considered in prior work. We present both theoretical analysis and exhaustive experimental results (on Amazon EC2 clusters) that demonstrate the performance advantages of our method. For the single and multiple job cases, we obtain speed-ups of 4.69x (and 2.6x over prior work) and 4.31x over the baseline approach, respectively.
Another approach that re-examines the computation - communication tradeoff from an alternate viewpoint has been investigated in @cite_9 . In this case, the assumption is that a server does not need to process all locally available files and storage constraints do not necessarily imply computation constraints. A lower bound on the was derived along with a heuristic scheme to achieve it in some cases.
@cite_9
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In this paper, we revisit the communication vs. distributed computing trade-off, studied within the framework of MapReduce in [1]. An implicit assumption in the aforementioned work is that each server performs all possible computations on all the files stored in its memory. Our starting observation is that, if servers can compute only the intermediate values they need, then storage constraints do not directly imply computation constraints. We examine how this affects the communication-computation trade-off and suggest that the trade-off be studied with a predetermined storage constraint. We then proceed to examine the case where servers need to perform computationally intensive tasks, and may not have sufficient time to perform all computations required by the scheme in [1]. Given a threshold that limits the computational load, we derive a lower bound on the associated communication load, and propose a heuristic scheme that achieves in some cases the lower bound. Scavenging the idling computation resources at the enormous number of mobile devices, ranging from small IoT devices to powerful laptop computers, can provide a powerful platform for local mobile cloud computing. The vision can be realized by peer-to-peer cooperative computing between edge devices, referred to as co-computing . This paper exploits the non-causal helper’s CPU-state information to design energy-efficient co-computing policies for scavenging time-varying spare computation resources at peer mobiles. Specifically, we consider a co-computing system where a user offloads computation of input data to a helper. The helper controls the offloading process for the objective of minimizing the user’s energy consumption based on a predicted helper’s CPU-idling profile that specifies the amount of available computation resource for co-computing. Consider the scenario that the user has one-shot input-data arrival and the helper buffers offloaded bits. The problem for energy-efficient co-computing is formulated as two sub-problems: the slave problem corresponding to adaptive offloading and the master one to data partitioning. Given a fixed offloaded data size, the adaptive offloading aims at minimizing the energy consumption for offloading by controlling the offloading rate under the deadline and buffer constraints. By deriving the necessary and sufficient conditions for the optimal solution, we characterize the structure of the optimal policies and propose algorithms for computing the policies. Furthermore, we show that the problem of optimal data partitioning for offloading and local computing at the user is convex, admitting a simple solution using the sub-gradient method. Finally, the developed design approach for co-computing is extended to the scenario of bursty data arrivals at the user accounting for data causality constraints. Simulation results verify the effectiveness of the proposed algorithms. Migrating computational intensive tasks from mobile devices to more resourceful cloud servers is a promising technique to increase the computational capacity of mobile devices while saving their battery energy. In this paper, we consider an MIMO multicell system where multiple mobile users (MUs) ask for computation offloading to a common cloud server. We formulate the offloading problem as the joint optimization of the radio resources—the transmit precoding matrices of the MUs—and the computational resources—the CPU cycles second assigned by the cloud to each MU—in order to minimize the overall users’ energy consumption, while meeting latency constraints. The resulting optimization problem is nonconvex (in the objective function and constraints). Nevertheless, in the single-user case, we are able to compute the global optimal solution in closed form. In the more challenging multiuser scenario, we propose an iterative algorithm, based on a novel successive convex approximation technique, converging to a local optimal solution of the original nonconvex problem. We then show that the proposed algorithmic framework naturally leads to a distributed and parallel implementation across the radio access points, requiring only a limited coordination signaling with the cloud. Numerical results show that the proposed schemes outperform disjoint optimization algorithms. We propose a unified coded framework for distributed computing with straggling servers, by introducing a tradeoff between "latency of computation" and "load of communication" for some linear computation tasks. We show that the coded scheme of [1]-[3] that repeats the intermediate computations to create coded multicasting opportunities to reduce communication load, and the coded scheme of [4], [5] that generates redundant intermediate computations to combat against straggling servers can be viewed as special instances of the proposed framework, by considering two extremes of this tradeoff: minimizing either the load of communication or the latency of computation individually. Furthermore, the latency-load tradeoff achieved by the proposed coded framework allows to systematically operate at any point on that tradeoff to perform distributed computing tasks. We also prove an information-theoretic lower bound on the latency-load tradeoff, which is shown to be within a constant multiplicative gap from the achieved tradeoff at the two end points. We consider a MIMO multicell system wherein several Mobile Users (MUs) ask for computation offloading to a common cloud server through their femto-access points. We formulate the computation offloading problem as a joint optimization of the radio resources??the transmit precoding matrices of the MUs??and the computational resources??the CPU cycles second assigned by the cloud to each MU??in order to minimize the overall users' energy consumption while meeting the latency constraints imposed by the applications running on the MUs. The resulting optimization problem is nonconvex (in the objective function and the constraints), and there are constraints coupling all the optimization variables. To cope with the nonconvexity, we hinge on successive convex approximation techniques and propose an iterative algorithm converging to a local optimal solution of the original nonconvex problem. The algorithm is also suitable for a parallel implementation across the access point, with limited coordination signaling with the cloud. Numerical results show that the proposed joint optimization yields significant energy savings with respect to more traditional schemes performing a separate optimization of the radio and computational resources. We consider the problem of storing segments of encoded versions of content files in a set of base stations located in a communication cell. These base stations work in conjunction with the main base station of the cell. Users move randomly across the space based on a discrete-time Markov chain model. At each time slot each user accesses a single base station based on it's current position and it can download only a part of the content stored in it, depending on the time slot duration. We assume that file requests must be satisfied within a given time deadline in order to be successful. If the amount of the downloaded (encoded) data by the accessed base stations when the time deadline expires does not suffice to recover the requested file, the main base station of the cell serves the request. Our aim is to find the storage allocation that minimizes the probability of using the main base station for file delivery. This problem is intractable in general. However, we show that the optimal solution of the problem can be efficiently attained in case that the time deadline is small. To tackle the general case, we propose a distributed approximation algorithm based on large deviation inequalities. Systematic experiments on a real world data set demonstrate the effectiveness of our proposed algorithms. Index Terms: Mobility-aware Caching, Markov Chain, MDS Coding, Small-cell Networks When delegating computation to a service provider, as in cloud computing, we seek some reassurance that the output is correct and complete. Yet recomputing the output as a check is inefficient and expensive, and it may not even be feasible to store all the data locally. We are therefore interested in proof systems which allow a service provider to prove the correctness of its output to a streaming (sublinear space) user, who cannot store the full input or perform the full computation herself. Our approach is two-fold. First, we describe a carefully chosen instantiation of one of the most efficient general-purpose constructions for arbitrary computations (streaming or otherwise), due to Goldwasser, Kalai, and Rothblum. This requires several new insights to make the methodology more practical. Our main contribution is in achieving a prover who runs in time O(S(n) log S(n)), where S(n) is the size of an arithmetic circuit computing the function of interest. Our experimental results demonstrate that a practical general-purpose protocol for verifiable computation may be significantly closer to reality than previously realized. Second, we describe techniques that achieve genuine scalability for protocols fine-tuned for specific important problems in streaming and database processing. Focusing in particular on non-interactive protocols for problems ranging from matrix-vector multiplication to bipartite perfect matching, we build on prior work to achieve a prover who runs in nearly linear-time, while obtaining optimal tradeoffs between communication cost and the user's working memory. Existing techniques required (substantially) superlinear time for the prover. We argue that even if general-purpose methods improve, fine-tuned protocols will remain valuable in real-world settings for key problems, and hence special attention to specific problems is warranted. In this paper, we study the problem of reducing the delay of downloading data from cloud storage systems by leveraging multiple parallel threads, assuming that the data has been encoded and stored in the clouds using fixed rate forward error correction (FEC) codes with parameters (n, k). That is, each file is divided into k equal-sized chunks, which are then expanded into n chunks such that any k chunks out of the n are sufficient to successfully restore the original file. The model can be depicted as a multiple-server queue with arrivals of data retrieving requests and a server corresponding to a thread. However, this is not a typical queueing model because a server can terminate its operation, depending on when other servers complete their service (due to the redundancy that is spread across the threads). Hence, to the best of our knowledge, the analysis of this queueing model remains quite uncharted. Recent traces from Amazon S3 show that the time to retrieve a fixed size chunk is random and can be approximated as a constant delay plus an i.i.d. exponentially distributed random variable. For the tractability of the theoretical analysis, we assume that the chunk downloading time is i.i.d. exponentially distributed. Under this assumption, we show that any work-conserving scheme is delay-optimal among all on-line scheduling schemes when k = 1. When k > 1, we find that a simple greedy scheme, which allocates all available threads to the head of line request, is delay optimal among all on-line scheduling schemes. We also provide some numerical results that point to the limitations of the exponential assumption, and suggest further research directions. We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it lower bounds the information complexity of any function. Our relaxed partition bound subsumes all norm based methods (e.g. the ?2 method) and rectangle-based methods (e.g. the rectangle corruption bound, the smooth rectangle bound, and the discrepancy bound), except the partition bound. Our result uses a new connection between rectangles and zero-communication protocols where the players can either output a value or abort. We prove the following compression lemma: given a protocol for a function f with information complexity I, one can construct a zero-communication protocol that has non-abort probability at least 2^ -O(I) and that computes f correctly with high probability conditioned on not aborting. Then, we show how such a zero-communication protocol relates to the relaxed partition bound. We use our main theorem to resolve three of the open questions raised by Braver man. First, we show that the information complexity of the Vector in Subspace Problem is O(n^ 1 3 ), which, in turn, implies that there exists an exponential separation between quantum communication complexity and classical information complexity. Moreover, we provide an O(n) lower bound on the information complexity of the Gap Hamming Distance Problem. We consider load balancing in a network of caching servers delivering contents to end users. Randomized load balancing via the so-called power of two choices is a well-known approach in parallel and distributed systems. In this framework, we investigate the tension between storage resources, communication cost, and load balancing performance. To this end, we propose a randomized load balancing scheme which simultaneously considers cache size limitation and proximity in the server redirection process. In contrast to the classical power of two choices setup, since the memory limitation and the proximity constraint cause correlation in the server selection process, we may not benefit from the power of two choices. However, we prove that in certain regimes of problem parameters, our scheme results in the maximum load of order @math (here @math is the network size). This is an exponential improvement compared to the scheme which assigns each request to the nearest available replica. Interestingly, the extra communication cost incurred by our proposed scheme, compared to the nearest replica strategy, is small. Furthermore, our extensive simulations show that the trade-off trend does not depend on the network topology and library popularity profile details. This letter considers a mobile edge computing system with one access point (AP) serving multiple users over a multicarrier channel, in the presence of a malicious eavesdropper. In this system, each user can execute the respective computation tasks by partitioning them into two parts, which are computed locally and offloaded to AP, respectively. We exploit the physical-layer security to secure the multiuser computation offloading from being overheard by the eavesdropper. Under this setup, we minimize the weighted sum-energy consumption for these users, subject to the newly imposed secrecy offloading rate constraints and the computation latency constraints, by jointly optimizing their computation and communication resource allocations. We propose an efficient algorithm to solve this problem. Video on-demand streaming from Internet-based servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as "helpers"). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of @math , where @math is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes. In this paper we examine the problem of sending an n-bit data item from a client to a server across an asymmetric communication channel. We demonstrate that there are scenarios in which a high-speed link from the server to the client can be used to greatly reduce the number of bits sent from the client to the server across a slower link. In particular, we assume that the data item is drawn from a probability distribution D that is known to the server but not to the client. We present several protocols in which the expected number of bits transmitted by the server and client are O(n) and O(H(D)+1), respectively, where H(D) is the binary entropy of D (and can range from 0 to n). These protocols are within a small constant factor of optimal in terms of the number of bits sent by the client. The expected number of rounds of communication between the server and client in the simplest of our protocols is O(H(D)). We also give a protocol for which the expected number of rounds is only O(1), but which requires more computational effort on the part of the server. A third technique provides a tradeoff between the computational effort and the number of rounds. These protocols are complemented by several lower bounds and impossibility results. We prove that all of our protocols are existentially optimal in terms of the number of bits sent by the server, i.e., there are distributions for which the total number of bits exchanged has to be at least n. In addition, we show that there is no protocol that is optimal for every distribution (as opposed to just existentially optimal) in terms of bits sent by the server. We demonstrate this by proving that it is undecidable to compute (even approximately), for an arbitrary distribution D, the expected number of bits that must be exchanged by the server and client on the distribution D. Video on-demand streaming from Internet-based servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as “helpers”). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of 1-(1-1 d )d, where d is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes. We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem, where copies of a file may be be stored in the local storage of some subsets of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for on-line data tracking (a generalization of mobile user tracking) to transform our competitive data management algorithms into distributed algorithms themselves. Designing mobile edge computing (MEC) systems by jointly optimizing communication and computation resources, which can help increase mobile batteries' lifetime and improve quality of experience for computation-intensive and latency-sensitive applications, has received significant interest. In this paper, we consider energy-efficient resource allocation schemes for a multi-user mobile edge computing system with inelastic computation tasks and non-negligible task execution durations. First, we establish a mathematical model to characterize the offloading of a computation task from a mobile to the base station (BS) equipped with MEC servers. This computation-offloading model consists of three stages, i.e., task uploading, task executing, and computation result downloading, and allows parallel transmissions and executions for different tasks. Then, we formulate the weighted sum energy consumption minimization problem to optimally allocate the task operation sequence, the uploading and downloading time durations as well as the starting times for uploading, executing and downloading, which is a challenging mixed discrete- continuous optimization problem and is NP-hard in general. We propose a method to obtain an optimal solution and develop a low-complexity algorithm to obtain a suboptimal solution, by connecting the optimization problem to a three-stage flow-shop scheduling problem and utilizing Johnson's algorithm as well as convex optimization techniques. Finally, numerical results show that the proposed sub-optimal solution outperforms existing comparison schemes. We revisit the classic problem of spreading a piece of information in a group of @math n fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasieniec and Pelc (Parallel Comput 22:903---912, 1996), we derive for the first time protocols that (i) use a linear number of messages, (ii) are correct even when an arbitrary number of adversarially chosen processors does not participate in the process, and (iii) with high probability have the asymptotically optimal runtime of @math O(logn) when at least an arbitrarily small constant fraction of the processors are working. In addition, our protocols do not require that the system is synchronized nor that all processors are simultaneously woken up at time zero, they are fully based on push-operations, and they do not need an a priori estimate on the number of failed nodes. Our protocols thus overcome the typical disadvantages of the two known approaches, algorithms based on random gossip (typically needing a large number of messages due to their unorganized nature) and algorithms based on fair workload splitting (which are either not time-efficient or require intricate preprocessing steps plus synchronization). Abstract With the rapid increase in the development of the Internet of Things and 5G networks in the smart city context, a large amount of data (i.e., big data) is expected to be generated, resulting in increased latency for the traditional cloud computing paradigm. To reduce the latency, mobile edge computing has been considered for offloading a part of the workload from mobile devices to nearby edge servers that have sufficient computation resources. Although there has been significant research in the field of mobile edge computing, little attention has been given to understanding the placement of edge servers in smart cities to optimize the mobile edge computing network performance. In this paper, we study the edge server placement problem in mobile edge computing environments for smart cities. First, we formulate the problem as a multi-objective constraint optimization problem that places edge servers in some strategic locations with the objective to make balance the workloads of edge servers and minimize the access delay between the mobile user and edge server. Then, we adopt mixed integer programming to find the optimal solution. Experimental results based on Shanghai Telecom’s base station dataset show that our approach outperforms several representative approaches in terms of access delay and workload balancing. In this paper, we study resource allocation for multiuser multiple-input–single-output secondary communication systems with multiple system design objectives. We consider cognitive radio (CR) networks where the secondary receivers are able to harvest energy from the radio frequency when they are idle. The secondary system provides simultaneous wireless power and secure information transfer to the secondary receivers. We propose a multiobjective optimization framework for the design of a Pareto-optimal resource allocation algorithm based on the weighted Tchebycheff approach. In particular, the algorithm design incorporates three important system design objectives: total transmit power minimization, energy harvesting efficiency maximization, and interference-power-leakage-to-transmit-power ratio minimization. The proposed framework takes into account a quality-of-service (QoS) requirement regarding communication secrecy in the secondary system and the imperfection of the channel state information (CSI) of potential eavesdroppers (idle secondary receivers and primary receivers) at the secondary transmitter. The proposed framework includes total harvested power maximization and interference power leakage minimization as special cases. The adopted multiobjective optimization problem is nonconvex and is recast as a convex optimization problem via semidefinite programming (SDP) relaxation. It is shown that the global optimal solution of the original problem can be constructed by exploiting both the primal and the dual optimal solutions of the SDP-relaxed problem. Moreover, two suboptimal resource allocation schemes for the case when the solution of the dual problem is unavailable for constructing the optimal solution are proposed. Numerical results not only demonstrate the close-to-optimal performance of the proposed suboptimal schemes but unveil an interesting tradeoff among the considered conflicting system design objectives as well. In this paper, we prove a lower bound on the number of rounds required by a deterministic distributed protocol for broadcasting a message in radio networks whose processors do not know the identities of their neighbors. Such an assumption captures the main characteristic of mobile and wireless environments [3], i.e., the instability of the network topology. For any distributed broadcast protocol II, for any n and for any D ≤ n 2, we exhibit a network G with n nodes and diameter D such that the number of rounds needed by H for broadcasting a message in G is Ω(D log n). The result still holds even if the processors in the network use a different program and know n and D. We also consider the version of the broadcast problem in which an arbitrary number of processors issue at the same time an identical message that has to be delivered to the other processors. In such a case we prove that, even assuming that the processors know the network topology, Ω(n) rounds are required for solving the problem on a complete network (D=1) with n processors.