Practical Compact Routing on Sparse Graphs

We describe a simple and practical algorithm for compact routing on graphs which admit compact and balanced vertex separators. Using a recursive nested dissection of then-vertex graph based on these separators, we construct routing tables with as few as O(log n) entries per vertex in a preprocessing step. They support handshaking-based routing on the graph with moderate stretch, where the handshaking can be implemented similarly to a DNS lookup. We describe a basic version of the algorithm that requires modifiable headers and a more advanced version which eliminates this need and provides better stretch. A number of algorithmic parameters control a graceful tradeoff between the size of the routing tables and the stretch. Our routing algorithm is most effective on planar graphs and unit disk graphs of moderate edge/vertex density.

Practical Compact Routing on Sparse Graphs

We describe a simple and practical algorithm for compact routing on graphs which admit compact and balanced vertex separators. Using a recursive nested dissection of then-vertex graph based on these separators, we construct routing tables with as few as O(log n) entries per vertex in a preprocessing step. They support handshaking-based routing on the graph with moderate stretch, where the handshaking can be implemented similarly to a DNS lookup. We describe a basic version of the algorithm that requires modifiable headers and a more advanced version which eliminates this need and provides better stretch. A number of algorithmic parameters control a graceful tradeoff between the size of the routing tables and the stretch. Our routing algorithm is most effective on planar graphs and unit disk graphs of moderate edge/vertex density.

Mathematical model and algorithm for calculating the cycles of the cells of the graph map

Выделенные свойства циклов DFS-базиса блока карты простого графа позволили составить математическую модель вычисления циклов ячеек карты графа. По данной модели предложен практический алгоритм вычисления циклов ячеек карты графа. Алгоритм имеет квадратическую сложность относительно числа вершин в графе. The selected properties of the cycles of the DFS-basis block of a simple graph map allowed us to create a mathematical model for calculating the cycles of the cells of the graph map. According to this model, a practical algorithm for calculating the cycles of the graph map cells is proposed. The algorithm has a quadratic complexity relative to the number of vertices in the graph.

Magnet Ingestion in Children Management Guidelines and Prevention

Purpose: Foreign body ingestion is common in children, and most foreign bodies pass spontaneously without causing serious injuries. Ingestion of multiple high-power magnet pieces is unique and increases the risk of morbidity and mortality. The longer the duration of ingestion, the increased likelihood of complications. Various management options have been reported, and there is no consensus on the ideal management which necessitates the need for a practical algorithm. The incidence of magnet ingestion has been increasing and directly related to the laws and recalls. The aim of this review is to provide an easy and practical pathway for management and to highlight the preventive rules of the legislations and recalls.Methods: PubMed/MEDLINE, the Cochrane Database of Systematic Reviews, and the list of references from all identified complete publications were searched for all publications in English-language for pediatric magnet ingestion.Conclusion: Practical and time-saving management pathways are recommended to minimize the risk of complications. Preventive rules and recalls are important for eliminating the availability of these hazardous magnets. Public awareness about the unique risks posed by these magnets if ingested is important.

The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound

The Traveling Tournament Problem is a well-known benchmark problem in tournament timetabling, which asks us to design a schedule of home/away games of n teams (n is even) under some feasibility requirements such that the total traveling distance of all the n teams is minimized. In this paper, we study TTP-2, the traveling tournament problem where at most two consecutive home games or away games are allowed, and give an effective algorithm for n/2 being odd. Experiments on the well-known benchmark sets show that we can beat previously known solutions for all instances with n/2 being odd by an average improvement of 2.66%. Furthermore, we improve the theoretical approximation ratio from 3/2+O(1/n) to 1+O(1/n) for n/2 being odd, answering a challenging open problem in this area.