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Finding heavy-elements (heavy-hitters) in streaming data is one of the central, and well-understood tasks. Despite the importance of this problem, when considering the sliding windows model of streaming (where elements eventually expire) the problem of finding L 2 -heavy elements has remained completely open despite multiple papers and considerable success in finding L 1 -heavy elements. Since the L 2 -heavy element problem doesn't satisfy certain conditions, existing methods for sliding windows algorithms, such as smooth histograms or exponential histograms are not directly applicable to it. In this paper, we develop the first polylogarithmic-memory algorithm for finding L 2 -heavy elements in the sliding window model. Our technique allows us not only to find L 2 -heavy elements, but also heavy elements with respect to any L p with 0 < p ≤ 2 on sliding windows. By this we completely “close the gap” and resolve the question of finding L p -heavy elements in the sliding window model with polylogarithmic memory, since it is well known that for p > 2 this task is impossible. We demonstrate a broader applicability of our method on two additional examples: we show how to obtain a sliding window approximation of the similarity of two streams, and of the fraction of elements that appear exactly a specified number of times within the window (the α -rarity problem). In these two illustrative examples of our method, we replace the current expected memory bounds with worst case bounds. [ABSTRACT FROM AUTHOR]

In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items) arrive one by one, each item must be packed into a square bin of unit size on its arrival without any information about future items. When packing items, 90°-rotation is allowed. 1-space bounded means there is only one “active” bin. If the “active” bin cannot accommodate the coming item, it will be closed and a new bin will be opened. The objective is to minimize the total number of bins used for packing all items in the sequence. Our contributions are as follows: For 1-space bounded 2-dimensional bin packing, we propose an online packing algorithm with a tight competitive ratio of 5.06. A lower bound of 3.17 on the competitive ratio is proven. Moreover, we study 1-space bounded square packing, where each item is a square with side length no more than 1. A 4.3-competitive algorithm is achieved, and a lower bound of 2.94 on the competitive ratio is given. All these bounds surpass the previously best known results. [ABSTRACT FROM AUTHOR]

Recent research shows that significant energy saving can be achieved in wireless sensor networks (WSNs) with a mobile base station that collects data from sensor nodes via short-range communications. However, a major performance bottleneck of such WSNs is the significantly increased latency in data collection due to the low movement speed of mobile base stations. In this paper we study the problem of finding a data collection path for a mobile base station moving along a fixed track in a wireless sensor network to minimize the latency of data collection. The main contribution is an O ( m n log ⁡ n ) expected time algorithm, where n is the number of sensors in the networks and m is the complexity of the fixed track. [ABSTRACT FROM AUTHOR]