Linearizing Partial Search Orders

In recent years, questions about the construction of special orderings of a given graph search were studied by several authors. On the one hand, the so called end-vertex problem introduced by Corneil et al. in 2010 asks for search orderings ending in a special vertex. On the other hand, the problem of finding orderings that induce a given search tree was introduced already in the 1980s by Hagerup and received new attention most recently by Beisegel et al. Here, we introduce a generalization of some of these problems by studying the question whether there is a search ordering that is a linear extension of a given partial order on a graph's vertex set. We show that this problem can be solved in polynomial time on chordal bipartite graphs for LBFS, which also implies the first polynomial-time algorithms for the end-vertex problem and two search tree problems for this combination of graph class and search. Furthermore, we present polynomial-time algorithms for LBFS and MCS on split graphs which generalize known results for the end-vertex and search tree problems.Comment: full version of an extended abstract to be published in the Proceedings of the 48th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2022) in T\"ubinge

Graph Search Trees and Their Leaves

Graph searches and their respective search trees are widely used in algorithmic graph theory. The problem whether a given spanning tree can be a graph search tree has been considered for different searches, graph classes and search tree paradigms. Similarly, the question whether a particular vertex can be visited last by some search has been studied extensively in recent years. We combine these two problems by considering the question whether a vertex can be a leaf of a graph search tree. We show that for particular search trees, including DFS trees, this problem is easy if we allow the leaf to be the first vertex of the search ordering. We contrast this result by showing that the problem becomes hard for many searches, including DFS and BFS, if we forbid the leaf to be the first vertex. Additionally, we present several structural and algorithmic results for search tree leaves of chordal graphs.Comment: full version of an extended abstract to be published in the Proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2023) in Fribour

Measuring Efficiency of German Bus Public Transport

This paper quantifies the technical efficiency of German bus companies and elaborates on the main factors influencing their performance. Efficiency is measured with a stochastic production frontier. We test for the impact on efficiency of ownership structure and participation at tendering. Furthermore, we investigate the influence on efficiency when a bus company is a part of a multi-product enterprise. The results yield insights how public bus companies might improve their performance in order to cope with the changing market environment. The mean technical efficiency of the investigated bus companies is around 87 percent. Bus companies with participation at tendering show a significantly higher mean efficiency than other companies. The ownership structure has no influence on technical efficiency.Stochastic Frontier Analysis, Production Function, Public Transport, Efficiency Analysis,

Optimizing Traffic Signal Timings for Mega Events

Most approaches for optimizing traffic signal timings deal with the daily traffic. However, there are a few occasional events like football matches or concerts of musicians that lead to exceptional traffic situations. Still, such events occur more or less regularly and place and time are known in advance. Hence, it is possible to anticipate such events with special signal timings. In this paper, we present an extension of a cyclically time-expanded network flow model and a corresponding mixed-integer linear programming formulation for simultaneously optimizing traffic signal timings and traffic assignment for such events. Besides the mathematical analysis of this approach, we demonstrate its capabilities by computing signal timings for a real world scenario

Optimizing Traffic Signal Settings for Public Transport Priority

In order to promote public transport many municipalities use traffic signal control with a priority for buses or trams. In this paper, we address the problem of finding optimal passive transit signal priority settings. Building on a cyclically time-expanded network model for the combined traffic assignment traffic signal coordination problem, we introduce a suitable queuing model and several modifications to model public transport vehicles appropriately. We evaluate the applicability of this approach by computing and analyzing optimal solutions for several instances of a real-world scenario

Optimal Bicycle Routes with Few Signal Stops

With the increasing popularity of cycling as a mode of transportation, there is a growing need for efficient routing algorithms that consider the specific requirements of cyclists. This paper studies the optimization of bicycle routes while minimizing the number of stops at traffic signals. In particular, we consider three different types of stopping strategies and three types of routes, namely paths, trails, and walks. We present hardness results as well as a pseudo-polynomial algorithm for the problem of computing an optimal route with respect to a pre-defined stop bound

Linear Time LexDFS on Chordal Graphs

Lexicographic Depth First Search (LexDFS) is a special variant of a Depth First Search (DFS), which was introduced by Corneil and Krueger in 2008. While this search has been used in various applications, in contrast to other graph searches, no general linear time implementation is known to date. In 2014, K\"ohler and Mouatadid achieved linear running time to compute some special LexDFS orders for cocomparability graphs. In this paper, we present a linear time implementation of LexDFS for chordal graphs. Our algorithm is able to find any LexDFS order for this graph class. To the best of our knowledge this is the first unrestricted linear time implementation of LexDFS on a non-trivial graph class. In the algorithm we use a search tree computed by Lexicographic Breadth First Search (LexBFS)

Optimization and simulation of fixed-time traffic signal control in real-world applications

This paper contributes to the question how to optimize fixed-time traffic signal coordinations for real-world applications. Therefore, two models are combined: An analytically model that optimizes fixed-time plans based on a cyclically time-expanded network formulation, and a coevolutionary transport simulation that is able to evaluate the optimized fixed-time plans for large-scale realistic traffic situations. The coupling process of both models is discussed and applied to a real-world scenario. Steps that were necessary to align the models and improve the results are presented. The optimized fixed-time signals are compared to other signal approaches in the application. It is found, that they also help to improve the performance of actuated signal control

Genomic resources for water yam (Dioscorea alata L.): analyses of EST sequences, De Novo sequencing and GBS libraries

Published online: 29 July 201