Randomized online computation with high probability guarantees

We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like paging, k-server and metrical task systems on finite metrics, and show that for these problems it is possible to obtain, given an algorithm with constant expected competitive ratio, another algorithm that achieves the same solution quality up to an arbitrarily small constant error a with high probability; the "high probability" statement is in terms of the optimal cost. Furthermore, we show that our assumptions are tight in the sense that removing any of them allows for a counterexample to the theorem. In addition, there are examples of other problems not covered by our definition, where similar high probability results can be obtained.Comment: 20 pages, 2 figure

Online Coded Caching

We consider a basic content distribution scenario consisting of a single origin server connected through a shared bottleneck link to a number of users each equipped with a cache of finite memory. The users issue a sequence of content requests from a set of popular files, and the goal is to operate the caches as well as the server such that these requests are satisfied with the minimum number of bits sent over the shared link. Assuming a basic Markov model for renewing the set of popular files, we characterize approximately the optimal long-term average rate of the shared link. We further prove that the optimal online scheme has approximately the same performance as the optimal offline scheme, in which the cache contents can be updated based on the entire set of popular files before each new request. To support these theoretical results, we propose an online coded caching scheme termed coded least-recently sent (LRS) and simulate it for a demand time series derived from the dataset made available by Netflix for the Netflix Prize. For this time series, we show that the proposed coded LRS algorithm significantly outperforms the popular least-recently used (LRU) caching algorithm.Comment: 15 page

Online Service with Delay

In this paper, we introduce the online service with delay problem. In this problem, there are $n$ points in a metric space that issue service requests over time, and a server that serves these requests. The goal is to minimize the sum of distance traveled by the server and the total delay in serving the requests. This problem models the fundamental tradeoff between batching requests to improve locality and reducing delay to improve response time, that has many applications in operations management, operating systems, logistics, supply chain management, and scheduling. Our main result is to show a poly-logarithmic competitive ratio for the online service with delay problem. This result is obtained by an algorithm that we call the preemptive service algorithm. The salient feature of this algorithm is a process called preemptive service, which uses a novel combination of (recursive) time forwarding and spatial exploration on a metric space. We hope this technique will be useful for related problems such as reordering buffer management, online TSP, vehicle routing, etc. We also generalize our results to $k > 1$ servers.Comment: 30 pages, 11 figures, Appeared in 49th ACM Symposium on Theory of Computing (STOC), 201

Context-aware Cluster Based Device-to-Device Communication to Serve Machine Type Communications

Billions of Machine Type Communication (MTC) devices are foreseen to be deployed in next ten years and therefore potentially open a new market for next generation wireless network. However, MTC applications have different characteristics and requirements compared with the services provided by legacy cellular networks. For instance, an MTC device sporadically requires to transmit a small data packet containing information generated by sensors. At the same time, due to the massive deployment of MTC devices, it is inefficient to charge their batteries manually and thus a long battery life is required for MTC devices. In this sense, legacy networks designed to serve human-driven traffics in real time can not support MTC efficiently. In order to improve the availability and battery life of MTC devices, context-aware device-to-device (D2D) communication is exploited in this paper. By applying D2D communication, some MTC users can serve as relays for other MTC users who experience bad channel conditions. Moreover, signaling schemes are also designed to enable the collection of context information and support the proposed D2D communication scheme. Last but not least, a system level simulator is implemented to evaluate the system performance of the proposed technologies and a large performance gain is shown by the numerical results