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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)

- Wolfgang W. Bein, Lawrence L. Larmore, Shahram Latifi, Ivan Hal Sudborough
- Int. J. Found. Comput. Sci.
- 2002

- Wolfgang W. Bein, Peter Brucker, Arie Tamir
- Discrete Applied Mathematics
- 1985

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)

- Wolfgang W. Bein, Peter Brucker, James K. Park, Pramod K. Pathak
- Discrete Applied Mathematics
- 1995

- Wolfgang W. Bein, Lawrence L. Larmore, John Noga
- ESA
- 2007

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)

- Wolfgang W. Bein, Lawrence L. Larmore, John Noga, Rüdiger Reischuk
- Algorithmica
- 2009

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)

- Wolfgang W. Bein, Jerzy Kamburowski, Matthias F. Stallmann
- SIAM J. Comput.
- 1992

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)

- Wolfgang W. Bein, José R. Correa, Xin Han
- Theor. Comput. Sci.
- 2007

“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)

- Wolfgang W. Bein, Rudolf Fleischer, Lawrence L. Larmore
- Inf. Process. Lett.
- 2000

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)

- Doina Bein, Wolfgang W. Bein, Swathi Venigella
- IDC
- 2011

We study the problem of allocating memory of servers in a data center based on online requests for storage. Given an online sequence of storage requests and a cost associated with serving the request by allocating space on a certain server one seeks to select the minimum number of servers as to minimize total cost. We use two different algorithms and… (More)