Mirela Damian

The kinetic preprocessor KPP*/a software environment for solving chemical kinetics

Abstract The kinetic preprocessor (KPP) is a software tool that assists the computer simulation of chemical kinetic systems. The concentrations of a chemical system evolve in time according to the differential law of mass action kinetics. A computer simulation requires the implementation of the differential system and its numerical integration in time. KPP translates a specification of the chemical mechanism into fortran or c simulation code that implement the concentration time derivative function and its Jacobian, together with a suitable numerical integration scheme. Sparsity in Jacobian is carefully exploited in order to obtain computational efficiency. KPP incorporates a library with several widely used atmospheric chemistry mechanisms and users can add their own chemical mechanisms to the library. KPP also includes a comprehensive suite of stiff numerical integrators. The KPP development environment is designed in a modular fashion and allows for rapid prototyping of new chemical kinetic schemes as well as new numerical integration methods.

SPANNING PROPERTIES OF GRAPHS INDUCED BY DIRECTIONAL ANTENNAS

Let S be a set of points in the plane, such that the unit disk graph with vertex set S is connected. We address the problem of finding orientations and a minimum radius for directional antennas of a fixed cone angle placed at the points of S, such that the induced communication graph G[S] is a hop t-spanner of the unit disk graph for S (meaning that G[S] is strongly connected, and contains a directed path with at most t edges between any pair of points within unit distance). We consider problem instances in which antenna angles are bounded below by 120° and 90°. We show that, in the case of 120° angles, a radius of 5 suffices to establish a hop 4-spanner; and in the case of 90° angles, a radius of 7 suffices to establish a hop 5-spanner.

π/2-Angle Yao Graphs are Spanners

We show that the Yao graph Y 4 in the L 2 metric is a spanner with stretch factor \(8\sqrt{2}(29+23\sqrt{2})\).

Switching to directional antennas with constant increase in radius and hop distance

For any angle α < 2π, we show that any connected communication graph that is induced by a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a strongly connected communication graph, in which each transceiver in P is equipped with a directional antenna of angle α and radius rdir, for some constant rdir = rdir(α). Moreover, the new communication graph is a c-spanner of the original graph, for some constant c = c(α), with respect to number of hops.

Unfolding Manhattan Towers

We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4x5x1 refinement of the vertex grid.

YAO GRAPHS SPAN THETA GRAPHS

Yao and Theta graphs are defined for a given point set and a fixed integer k > 0. The space around each point is divided into k cones of equal angle, and each point is connected to a nearest neighbor in each cone. The difference between Yao and Theta graphs is in the way the nearest neighbor is defined: Yao graphs minimize the Euclidean distance between a point and its neighbor, and Theta graphs minimize the Euclidean distance between a point and the orthogonal projection of its neighbor on the bisector of the hosting cone. We prove that, corresponding to each edge of the Theta graph Θ6, there is a path in the Yao graph Y6 whose length is at most 8.82 times the edge length. Combined with the result of Bonichon et al., who prove an upper bound of 2 on the stretch factor of Θ6, we obtain an upper bound of 17.64 on the stretch factor of Y6.

An O(n log n)-time algorithm for the restriction scaffold assignment problem.

The restriction scaffold assignment problem takes as input two finite point sets S and T (with S containing more points than T ) and establishes a correspondence between points in S and points in T , such that each point in S maps to exactly one point in T and each point in T maps to at least one point in S. An algorithm is presented that finds a minimum-cost solution for this problem in O(n log n) time, provided that the points in S and T are restricted to lie on a line and the cost function delta is the L(1) metric. This algorithm runs in linear time, if S and T are presorted. This improves the previously best-known O(n (2))-time algorithm for this problem.

New and Improved Spanning Ratios for Yao Graphs

For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle &thetas; = 2π/k, and connects each point to a nearest neighbor in each cone. It is known for all Yao graphs, with the sole exception of Y5, whether or not they are geometric spanners. In this paper we close this gap by showing that for odd k ≥ 5, the spanning ratio of Yk is at most 1/(1−2sin(3&thetas;/8)), which gives the first constant upper bound for Y5, and is an improvement over the previous bound of 1/(1−2sin(&thetas;/2)) for odd k ≥ 7. We further reduce the upper bound on the spanning ratio for Y5 from 10.9 to 2 + √3 ≈ 3.74, which falls slightly below the lower bound of 3.79 established for the spanning ratio of ⊝5 (⊝-graphs differ from Yao graphs only in the way they select the closest neighbor in each cone). This is the first such separation between a Yao and ⊝-graph with the same number of cones. We also give a lower bound of 2.87 on the spanning ratio of Y5. Finally, we revisit the Y6 graph, which plays a particularly important role as the transition between the graphs (k > 6) for which simple inductive proofs are known, and the graphs (k ≤ 6) whose best spanning ratios have been established by complex arguments. Here we reduce the known spanning ratio of Y6 from 17.6 to 5.8, getting closer to the spanning ratio of 2 established for ⊝6.

Coverage with k-transmitters in the presence of obstacles

For a fixed integer k≥0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower and upper bounds for the number of k-transmitters that are necessary and sufficient to cover a given collection of line segments, polygonal chains and polygons.

Establishing strong connectivity using optimal radius half-disk antennas

Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle @a>=180^o, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that r=3 if @a@?[180^o,240^o), r=2 if @a@?[240^o,270^o), r=2sin(36^o) if @a@?[270^o,288^o), and r=1 if @a>=288^o suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree of S is 1. These results are worst-case optimal and match the lower bounds presented in [I. Caragiannis, C. Kaklamanis, E. Kranakis, D. Krizanc, A. Wiese, Communication in wireless networks with directional antennae, in: Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, 2008, pp. 344-351]. In contrast, r=2 is sometimes necessary when @a<180^o.