We design a randomized online algorithm for k-server on binary trees with hierarchical edge lengths, with expected competitive ratio O(log ∆), where ∆ is the diameter of the metric. This is one of the first k-server algorithms with competitive ratio poly-logarithmic in the natural problem parameters, and represents substantial progress on the randomized k-server conjecture. Extending the algorithm to trees of higher degree would give a competitive ratio of O(log 2 ∆ log n) for the k-server problem on general metrics with n points and diameter ∆.

We explore a novel online packet scheduling model related to energy-efficiency in mobile data transport. This model incorporates multiple networks with non-persistent connectivities where we only know which networks are available in the current timestep. When a packet arrives, it specifies a deadline and, for each network, a value it is worth if sent over that network. Our goal is to maximize the total value of packets we send by their deadlines. To encourage energy-efficiency, our model requires that packets have larger values for more energyefficient networks. We demonstrate low-constant-competitive algorithms for this problem and several restrictions. We also provide lower bounds which closely match our competitive ratios and, under some restrictions, are tight.

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Abstract-We explore a novel online packet scheduling model related to energy-efficiency in mobile data transport. This model incorporates multiple networks with non-persistent connectivities where we only know which networks are available in the current timestep. When a packet arrives, it specifies a deadline and, for each network, a value it is worth if sent over that network. Our goal is to maximize the total value of packets we send by their deadlines. To encourage energy-efficiency, our model requires that packets have larger values for more energyefficient networks. We demonstrate low-constant-competitive algorithms for this problem and several restrictions. We also provide lower bounds which closely match our competitive ratios and, under some restrictions, are tight.