On hamiltonian colorings of block graphs

A hamiltonian coloring c of a graph G of order p is an assignment of colors to the vertices of G such that $D(u,v)+|c(u)-c(v)|\geq p-1$ for every two distinct vertices u and v of G, where D(u,v) denoted the detour distance between u and v. The value hc(c) of a hamiltonian coloring c is the maximum color assigned to a vertex of G. The hamiltonian chromatic number, denoted by hc(G), is the min{hc(c)} taken over all hamiltonian coloring c of G. In this paper, we present a lower bound for the hamiltonian chromatic number of block graphs and give a sufficient condition to achieve the lower bound. We characterize symmetric block graphs achieving this lower bound. We present two algorithms for optimal hamiltonian coloring of symmetric block graphs.Comment: 12 pages, 1 figure. A conference version appeared in the proceedings of WALCOM 201

Formats of Winning Strategies for Six Types of Pushdown Games

The solution of parity games over pushdown graphs (Walukiewicz '96) was the first step towards an effective theory of infinite-state games. It was shown that winning strategies for pushdown games can be implemented again as pushdown automata. We continue this study and investigate the connection between game presentations and winning strategies in altogether six cases of game arenas, among them realtime pushdown systems, visibly pushdown systems, and counter systems. In four cases we show by a uniform proof method that we obtain strategies implementable by the same type of pushdown machine as given in the game arena. We prove that for the two remaining cases this correspondence fails. In the conclusion we address the question of an abstract criterion that explains the results

3D Dynamic Motion Planning for Robot-Assisted Cannula Flexible Needle Insertion into Soft Tissue

In robot-assisted needle-based medical procedures, insertion motion planning is a crucial aspect. 3D dynamic motion planning for a cannula flexible needle is challenging with regard to the nonholonomic motion of the needle tip, the presence of anatomic obstacles or sensitive organs in the needle path, as well as uncertainties due to the dynamic environment caused by the movements and deformations of the organs. The kinematics of the cannula flexible needle is calculated in this paper. Based on a rapid and robust static motion planning algorithm, referred to as greedy heuristic and reachability-guided rapidly-exploring random trees, a 3D dynamic motion planner is developed by using replanning. Aiming at the large detour problem, the convergence problem and the accuracy problem that replanning encounters, three novel strategies are proposed and integrated into the conventional replanning algorithm. Comparisons are made between algorithms with and without the strategies to verify their validity. Simulations showed that the proposed algorithm can overcome the above-noted problems to realize real-time replanning in a 3D dynamic environment, which is appropriate for intraoperative planning. © 2016 Author

Low-Stress Bicycling and Network Connectivity

For a bicycling network to attract the widest possible segment of the population, its most fundamental attribute should be low-stress connectivity, that is, providing routes between people’s origins and destinations that do not require cyclists to use links that exceed their tolerance for traffic stress, and that do not involve an undue level of detour. The objective of this study is to develop measures of low-stress connectivity that can be used to evaluate and guide bicycle network planning. We propose a set of criteria by which road segments can be classified into four levels of traffic stress (LTS). LTS 1 is suitable for children; LTS 2, based on Dutch bikeway design criteria, represents the traffic stress that most adults will tolerate; LTS 3 and 4 represent greater levels of stress. As a case study, every street in San Jose, California, was classified by LTS. Maps in which only bicycle-friendly links are displayed reveal a city divided into islands within which low-stress bicycling is possible, but separated from one another by barriers that can be crossed only by using high-stress links. Two points in the network are said to be connected at a given level of traffic stress if the subnetwork of links that do not exceed the specified level of stress connects them with a path whose length does not exceed a detour criterion (25% longer than the most direct path). For the network as a whole, we demonstrate two measures of connectivity that can be applied for a given level of traffic stress. One is “percent trips connected,” defined as the fraction of trips in the regional trip table that can be made without exceeding a specified level of stress and without excessive detour. This study used the home-to-work trip table, though in principle any trip table, including all trips, could be used. The second is “percent nodes connected,” a cruder measure that does not require a regional trip table, but measures the fraction of nodes in the street network (mostly street intersections) that are connected to each other. Because traffic analysis zones (TAZs) are too coarse a geographic unit for evaluating connectivity by bicycle, we also demonstrate a method of disaggregating the trip table from the TAZ level to census blocks. For any given TAZ, origins in the home-to-work trip table are allocated in proportion to population, while destinations are allocated based on land-use data. In the base case, the fraction of work trips up to six miles long that are connected at LTS 2 is 4.7%, providing a plausible explanation for the city’s low bicycling share. We show that this figure would almost triple if a proposed slate of improvements, totaling 32 miles in length but with strategically placed segments that provide low-stress connectivity across barriers, were implemented