Riko Jacob

Dynamic planar convex hull

In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure.

Formal-Language-Constrained Path Problems

Given an alphabet

Time-dependent networks as models to achieve fast exact time-table queries

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A distributed polylogarithmic time algorithm for self-stabilizing skip graphs

, a (directed) graph G whose edges are weighted and

Optimal sparse matrix dense vector multiplication in the I/O-model

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Multistage methods for freight train classification

-labeled, and a formal language

Algorithms for Centrality Indices

L\subseteq\Sigma^*

The computational complexity of delay management

, the formal-language-constrained shortest/simple path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) \in L

Railway Delay Management: Exploring Its Algorithmic Complexity

. Here l(p) denotes the unique word obtained by concatenating the

Online delay management on a single train line

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