We introduce a framework for reducing the number of comparisons performed in the deletion and minimum deletion operations for priority queues. In particular, we give a priority queue with constant cost per insertion and minimum finding, and logarithmic cost with at most logn + O(log logn) 1 comparisons per deletion and minimum deletion, improving over the bound of 2 logn + O(1) comparisons for ...

The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted to bipartite graphs. Regarding the upper bound, we show that for any graph of order n, its local minimum degree is at most 3 8 n + o(n) and n 4 + o(n) for bi...

A cactus is a simple data structure that represents all minimum cuts of a weighted, undi-rected graph in linear space. We describe the rst algorithm that can build a cactus from the asymptotically fastest deterministic algorithm that nds all minimum cuts in a weighted graph | the Hao-Orlin minimum cut algorithm. This improves the time to construct the cactus in graphs with n vertices and m edge...

We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to faster, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity min cost flow that culminates decades of efforts to match the complexity of the fastest strongly polynomial algorithm known for the assignment problem. Th...

We show that, using the L1 metric, the minimum Hausdorr distance under translation between two point sets of cardinality n in d-dimensional space can be computed in time O(n (4d?2)=3 log 2 n) for d > 3. Thus we improve the previous time bound of O(n 2d?2 log 2 n) due to Chew and Kedem. For d = 3 we obtain a better result of O(n 3 log 2 n) time by exploiting the fact that the union of n axis-par...

Dispersion, as the characteristic variation of refractive index with wavelength, is more pronounced, where the wavelength is approaching to the absorption band. In ultra-optical glasses, the nonlinear refractive index, concerning to the light intensity dependent phenomenon, becomes considerable. Here, two ultra-optical property glass systems; TiO2-Bi2O3-PbO (TBP...

We give a simple O(n3/2 log n) algorithm for finding a minimum weight odd circuit in planar graphs. By geometric duality, the same algorithm can be used to find minimum weight odd cuts. For general sparse graphs, the fastest known algorithms for these two problems take O(n2 log n) time and O(n3 log n) time, respectively. © 2004 Elsevier B.V. All rights reserved.

We introduce a framework for reducing the number of element comparisons performed in priority-queue operations. In particular, we give a priority queue which guarantees the worst-case cost of O(1) per minimum finding and insertion, and the worst-case cost of O(log n) with at most log n+O(1) element comparisons per minimum deletion and deletion, improving the bound of 2 logn+ O(1) on the number ...

Various parameters of graphs connected to sparse matrix factoriza-tion and other applications can be approximated using an algorithm of Leighton et al. that nds vertex separators of graphs. The approximate values of the parameters, which include minimum front size, treewidth, pathwidth, and minimum elimination tree height, are no more than O(logn) (minimum front size and treewidth) and O(log 2 ...