Wolfgang W. Bein

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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. This paper gives an O(n2"5) algorithm for minimizing node reductions, based on vertex(More)
It is shown that an acyclic multigraph with a single source and a single sink is series-parallel if and only if for arbitrary linear cost functions and arbitrary capacities the corresponding minimum cost flow problem can be solved by a greedy algorithm. Furthermore, for networks of this type with m edges and n vertices, two O(mn + m log m)-algorithms are(More)
The randomized k-paging algorithm Equitable given by Achlioptas et al. is Hk-competitive and uses O(k 2 log k) memory. This competitive ratio is best possible. The randomized algorithm RMark given by Fiat et al. is (2Hk − 1)-competitive, but only uses O(k) memory. Borodin and El Yaniv [6] list as an open question whether there exists an Hk-competitive(More)
We introduce the novel concept of knowledge states. The knowledge state approach can be used to construct competitive randomized online algorithms and study the trade-off between competitiveness and memory. Many well-known algorithms can be viewed as knowledge state algorithms. A knowledge state consists of a distribution of states for the algorithm,(More)
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 problems(More)
An efficient randomized online algorithm for the paging problem for cache size 2 is given, which is 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)