Higher Order City Voronoi Diagrams

We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural complexity of kth-order city Voronoi diagrams of n point sites, we show an upper bound of O(k(n - k) + kc) and a lower bound of {\Omega}(n + kc), where c is the complexity of the transportation network. This is quite different from the bound O(k(n - k)) in the Euclidean metric. For the special case where k = n - 1 the complexity in the Euclidean metric is O(n), while that in the city metric is {\Theta}(nc). Furthermore, we develop an O(k^2(n + c) log n)-time iterative algorithm to compute the kth-order city Voronoi diagram and an O(nc log^2(n + c) log n)-time divide-and-conquer algorithm to compute the farthest-site city Voronoi diagram.Comment: 15 pages, extended version of paper to appear in Proc. 13th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT'12), Helsinki, Finland, 201

Placing Arrows in Directed Graph Drawings

We consider the problem of placing arrow heads in directed graph drawings without them overlapping other drawn objects. This gives drawings where edge directions can be deduced unambiguously. We show hardness of the problem, present exact and heuristic algorithms, and report on a practical study.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Trajectory-Based Dynamic Map Labeling

In this paper we introduce trajectory-based labeling, a new variant of dynamic map labeling, where a movement trajectory for the map viewport is given. We define a general labeling model and study the active range maximization problem in this model. The problem is NP-complete and W[1]-hard. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms. For the general case we present a practical ILP formulation with an experimental evaluation as well as approximation algorithms.Comment: 19 pages, 7 figures, extended version of a paper to appear at ISAAC 201

Contribution of immunoglobulins M and G, complement, and properdin to the intracellular killing of Escherichia coli by polymorphonuclear leukocytes

The effect of immunoglobulins and complement (C) on phagocytosis and intracellular killing of Escherichia coli was studied in vitro. The incubation system consisted of monolayers of human polymorphonuclear leukocytes and C-resistant, [3H]thymidine-labeled E. coli C source was human serum deprived of immunoglobulins and properdin by immunoabsorption. In the absence of C, only immunoglobulin G-coated bacteria were phagocytosed, whereas immunoglobulin M lacked opsonic activity. In the presence of C, phagocytosis was enhanced; however, immunoglobulin M was now more efficient than immunoglobulin G. Intracellular killing was notably augmented when C was activated by immunoglobulin G- or immunoglobulin M-coated bacteria; in contrast, the alternative activation of C by properdin had no effect on phagocytosis or intracellular killing. These results demonstrate the importance of immunoglobulins together with C not only for phagocytosis but also for efficient intracellular killing.</jats:p