Asynchronous Distributed Algorithms for Static and Dynamic Directed Rooted Graphs

Abstract

The paper provides a review of distributed graph algorithms research conducted by authors. We consider an asynchronous distributed system model represented by a strongly connected directed rooted graph with bounded edge capacity (in a sense that only a bounded number of messages can be sent through an edge in a given time interval). A graph can be static or dynamic, i.e. changing. For a static graph we propose a spanning (in- and out-) tree construction algorithm of time complexity O ( n / k + d ), requiring O ( n d log D+) message size and the same size of memory of each computing agent located in graph vertex, where n is the number of vertices of the graph, k is the capacity of an edge, d is the maximum length of simple path in the graph, D+ is the maximum outdegree of the vertices. The spanning trees constructed can be used in distributed computation of a function of the multiset of values assigned to graph vertices in a time not greater than 3 d . In a dynamic graph we suppose that k = 1 and an edge can appear, disappear, or change its end. We propose a dynamic graph monitoring algorithm than delivers information on any change to the root of the graph in O (n) or O ( d ) after the changes are stopped. We also propose graph exploration and marking algorithm with time complexity O ( n ). The marking provided by it is used in distributed computation of a function of the multiset of values assigned to dynamic graph vertices, which can be performed in time O ( n2) with messages of size O ( log n ) or in time O ( n ) with messages of size O ( n log n ).

Keywords

• распределенные алгоритмы
• асинхронные системы
• ориентированный граф
• корневой граф
• динамический граф
• параллельные вычисления