A distributed algorithm for constructing an Eulerian tour
نویسنده
چکیده
We present an efficient distributed algorithm for constructing an Eulerian tour in a network. To construct an Eulerian circuit the algorithm requires (1 + r)(IEI + IVl) messages and time units, where IEI is the number of the communication links, IVl is the number of the nodes in the underlying network graph, and 0 5 r < 1 . The value of r depends on the network topology and on the chosen traversal path. In the best case, when r = 0 the algorithm only requires (IEI + IVl) messages and time units. A simple modification allows us to construct a (noncyclic) tour using (1 + r)(IEI + 2lVl) messages and time units.
منابع مشابه
Eulerian tour algorithms for data visualization and the PairViz package
PairViz is an R package that produces orderings of statistical objects for visualization purposes. We abstract the ordering problem to one of constructing edge-traversals of (possibly weighted) graphs. PairViz implements various edge traversal algorithms which are based on Eulerian tours and Hamiltonian decompositions. We describe these algorithms, their PairViz implementation and discuss their...
متن کاملHeuristics for the Stochastic Eulerian Tour Problem
The Stochastic Eulerian Tour Problem (SETP) seeks the Eulerian tour of minimum expected length on an undirected Eulerian graph, when demand on the arcs that have to be serviced is probabilistic. In an earlier paper, we have shown that the SETP is NP-hard and derived several properties of the optimal tour. In this paper, we develop three constructive heuristics for the SETP. The first two are gr...
متن کاملThe Stochastic Eulerian Tour Problem
This paper defines the Stochastic Eulerian Tour Problem (SETP) and investigates several characteristics of this problem. Given an undirected Eulerian graph , a subset =) of the edges in E that require service, and a probability distribution for the number of edges in R that have to be visited in any given instance of the graph, the SETP seeks an a priori Eulerian tour of minimum expected length...
متن کاملINTEGRATING CASE-BASED REASONING, KNOWLEDGE-BASED APPROACH AND TSP ALGORITHM FOR MINIMUM TOUR FINDING
Imagine you have traveled to an unfamiliar city. Before you start your daily tour around the city, you need to know a good route. In Network Theory (NT), this is the traveling salesman problem (TSP). A dynamic programming algorithm is often used for solving this problem. However, when the road network of the city is very complicated and dense, which is usually the case, it will take too long fo...
متن کاملA 4/3-approximation for TSP on cubic 3-edge-connected graphs
We consider the travelling salesman problem on metrics which can be viewed as the shortest path metric of an undirected graph with unit edge-lengths. Finding a TSP tour in such a metric is then equivalent to finding a connected Eulerian subgraph in the underlying graph. Since the length of the tour is the number of edges in this Eulerian subgraph our problem can equivalently be stated as follow...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004