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Algorithms for series-parallel graphs can be extended to arbitrary two-terminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit in-degree (out-degree) into its sole incoming (outgoing) neighbor. We give an O(n 2:5) algorithm for minimizing node reductions, based on vertex cover in a… (More)

" Bin packing with rejection " is the following problem: Given a list of items with associated sizes and rejection costs, find a packing into unit bins of a subset of the list such that the number of bins used plus the sum of rejection costs of unpacked items is minimized. We show that bin packing with rejection can be reduced to n multiple knapsack… (More)

A class of " simple " online algorithms for the k-server problem is identified. This class, for which the term trackless is introduced, includes many known server algorithms. The k-server conjecture fails for trackless algorithms. A lower bound of 23/11 on the competitiveness of any deterministic trackless 2-server algorithm and a lower bound of 1 + √ 2/2… (More)

An efficient randomized online algorithm for the paging problem for cache size 2 is given, which is 3 2-competitive against an oblivious adversary. The algorithm keeps track of at most one page in slow memory at any time. A lower bound of 37 24 ≈ 1.5416 is given for the competitiveness of any trackless online algorithm for the same problem, i.e., an… (More)

We study the coverage problem for sensor networks from the fault tolerance and reliability point of view. Fault tolerance is a critical issue for sensors deployed in places where they are not easily replaceable, repairable and rechargeable. Failure of one node should not incapacitate the entire network. We propose three 1-fault tolerant topologies, namely… (More)

Batching has been studied extensively in the offline case, but applications such as manufacturing or TCP acknowledgment often require online solutions. We consider online batching problems, where the order of jobs to be batched is fixed and where we seek to minimize the sum of the completion times of the jobs. We present optimally competitive online… (More)