Some fixed point theorems and common fixed point theorem in Logarithmic convex structure areproved.

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure req...

We consider the problem of reporting convex hull points in an orthogonal range query in two dimensions. Formally, let P be a set of n points in R. A point lies on the convex hull of a point set S if it lies on the boundary of the minimum convex polygon formed by S. In this paper, we are interested in finding the points that lie on the boundary of the convex hull of the points in P that also fal...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

An important class of planar straight-line drawings of graphs are convex drawings, in which all the faces are drawn as convex polygons. A planar graph is said to be convex planar if it admits a convex drawing. We give a new combinatorial characterization of convex planar graphs based on the decomposition of a biconnected graph into its triconnected components. We then consider the problem of te...

Previous work has examined structure learning in log-linear models with `1regularization, largely focusing on the case of pairwise potentials. In this work we consider the case of models with potentials of arbitrary order, but that satisfy a hierarchical constraint. We enforce the hierarchical constraint using group `1-regularization with overlapping groups. An active set method that enforces h...