SUMMARY In this paper we study the resource allocation problem for the multiuser orthogonal frequency division multiplexing (OFDM)‐based cognitive radio (CR) systems with proportional rate constraints. The mutual interference introduced by primary user (PU) and cognitive radio user (also referred to secondary user, SU) makes the optimization problem of CR systems more complex. Moreover, the interference introduced to PUs must be kept under a given threshold. In this paper, the highest achievable rate of each OFDM subchannel is calculated by jointly considering the channel gain and interference level. First, a subchannel is assigned to the SU with the highest achievable rate. The remaining subchannels are always allocated to the SU that suffers the severest unjustness. Second, an efficient bit allocation algorithm is developed to maximize the sum capacity, which is again based on the highest achievable rate of each subchannel. Finally, an adjustment procedure is designed to maintain proportional fairness. Simulation results show that the proposed algorithm maximizes the sum capacity while keeping the proportional rate constraints satisfied. The algorithm exhibits a good tradeoff between sum capacity maximization and proportional fairness. Furthermore, the proposed algorithm has lower complexity compared with other algorithms, rendering it promising for practical applications. Copyright © 2011 John Wiley & Sons, Ltd.
Online social network (OSN) queries require retrievals of multiple small records generated by different users in the network, and the set of records to be retrieved is time dependent. Current implementation of hash-based partitioning results in accesses at a large number of servers, which significantly degrades response time. Partitioning the OSN friendship graph is difficult as its power-law degree distribution leads to many cross-partition edges. Naive replication requires extra storage that is orders of magnitude larger. In our previous work (2011), we proposed to partition not only the spatial network of social relations, but also in the time dimension so that users who have communicated in a given period are grouped together. We built an activity prediction graph (APG) to keep in one partition newly created data that are highly likely to be accessed together. In this paper, we analyze the distribution of the Facebook wall posts in the New Orleans network. We further emphasize that the objective of partitioning is to keep the two-hop neighborhood of a user in one partition, instead of the one-hop network usually considered. Two-hop neighborhoods are the basic units of retrieval in OSN and can be much larger than one-hop networks. We use a static partitioning method based on KMETIS, and a dynamic local partitioning method that maintains evenness and requires only a small amount of data movement across partitions. For evaluation, the partitioning results are tested with emulation of Facebook page downloads. We show that partitioning on twohop networks yields at lest 19% more local queries than its one-hop counterpart. The static algorithm achieves 5.6 times better data locality than hash-based partitioning and the dynamic algorithm achieves 6.4 times better locality while keeping the number of movements small. Almost all queries are kept in at most 3 partitions for both algorithms.
The clustering of vertices often evolves with time in a streaming graph, where graph update events are given as a stream of edge (vertex) insertions and deletions. Although a sliding window in stream processing naturally captures some cluster evolution, it alone may not be adequate, especially if the window size is large and the clustering within the windowed stream is unstable. Prior graph clustering approaches are mostly insensitive to clustering evolution. In this paper, we present an efficient approach to processing streaming graphs for evolution-aware clustering (EAC) of vertices. We incrementally manage individual connected components as clusters subject to a constraint on the maximal cluster size. For each cluster, we keep the relative recency of edges in a sorted order and favor more recent edges in clustering. We evaluate the effectiveness of EAC and compare it with a previous state-of-the-art evolution-insensitive clustering (EIC) approach. The results show that EAC is both effective and efficient in capturing evolution in a streaming graph. Moreover, we implement EAC as a streaming graph operator on IBM's InfoSphere Streams, a large-scale distributed middleware for stream processing, and show snapshots of the user cluster evolution in a streaming Twitter mention graph.
The generalized assignment problem (GAP) is NP-hard. It is even APX-hard to approximate it. The best known approximation algorithm is the LP-rounding algorithm in [1] with a (1− 1 e ) approximation ratio. We investigate the max-product belief propagation algorithm for the GAP, which is suitable for distributed implementation. The basic algorithm passes an exponential number of real-valued messages in each iteration. We show that the algorithm can be simplified so that only a linear number of real-valued messages are passed in each iteration. In particular, the computation of the messages from machines to jobs decomposes into two knapsack problems, which are also present in each iteration of the LP-rounding algorithm. The messages can be computed in parallel at each iteration. We observe that for small instances of GAP where the optimal solution can be computed, the message passing algorithm converges to the optimal solution when it is unique. We then show how to add small deterministic perturbations to ensure the uniqueness of the optimum. Finally, we prove GAP remains strongly NP-hard even if the optimum is unique.
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