Daniel J. Rosenkrantz

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Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line(More)
Several polynomial time algorithms finding “good,” but not necessarily optimal, tours for the traveling salesman problem are considered. We measure the closeness of a tour by the ratio of the obtained tour length to the minimal tour length. For the nearest neighbor method, we show the ratio is bounded above by a logarithmic function of the number of nodes.(More)
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We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance trade-off as the best known approximation schemes for planar graphs. We also define the concept of -precision unit disk(More)
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number k of nodes are required to be connected in the solution. A prototypical example is the kMST problem in which we require a tree of minimum weight spanning at least k nodes in an edge-weighted graph. We show(More)
We study several bicriteria network design problems phrased as follows: given an undirected graph and two minimization objectives with a budget specified on one objective, find a subgraph satisfying certain connectivity requirements that minimizes the second objective subject to the budget on the first. First, we develop a formalism for bicriteria problems(More)
A distributed database system is one in which the database is spread among several sites and application programs “move” from site to site to access and update the data they need. The concurrency control is that portion of the system that responds to the read and write requests of the application programs. Its job is to maintain the global(More)