Showing papers by "Rolf Fagerberg published in 1999"

Dynamic Representation of Sparse Graphs

Abstract: We present a linear space data structure for maintaining graphs with bounded arboricity--a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth--under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity.

Dynamic Representations of Sparse Graphs

Abstract: We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries.

The Complexity of Rebalancing a Binary Serach Tree

Abstract: For any function f, we give a rebalancing scheme for binary search trees which uses amortized O(f(n)) work per update while maintaining a height bounded by ⌊log(n + 1) + 1/f(n)⌋. This improves on previous algorithms for maintaining binary search trees of very small height, and matches an existing lower bound. The main implication is the exact characterization of the amortized cost of rebalancing binary search trees, seen as a function of the height bound maintained. We also show that in the semi-dynamic case, a height of ⌊log(n+1)⌋ can be maintained with amortized O(log n) work per insertion. This implies new results for TreeSort, and proves that it is optimal among all comparison based sorting algorithms for online sorting.