We consider a stateless ‘amnesiac’ variant of the stateful distributed network flooding algorithm, expanding on our conference papers [PODC’19, STACS’20]. Flooding begins with a set of source ‘initial’ nodes I seeking to broadcast a message M in rounds, in a network represented by an undirected graph (G, E) with set of nodes G and edges E. In every round, nodes with M send M to all neighbours from which they did not receive M in the previous round. Nodes do not remember earlier rounds, raising the possibility that M circulates indefinitely. Stateful flooding overcomes this by nodes recording every message circulated and ignoring M if received again. This overhead was assumed to be necessary. We show that almost optimal broadcast can still be achieved without this overhead. We prove that amnesiac flooding terminates on every finite graph and derive sharp bounds for termination times. Define (G, E) to be I-bipartite if the quotient graph, contracting all nodes in I to a single node, is bipartite. We prove that, if d is the diameter and e(I) the eccentricity of the set I, flooding terminates in e(I) rounds if (G, E) is I-bipartite and j rounds with e(I) < j \(\le \) \(e(I)+d+1 \le 2d +1\) if (G, E) is non I-bipartite. The separation in the termination times can be used for distributed discovery of topologies/distances in graphs. Termination is guaranteed if edges are lost during flooding but not, in general, if there is a delay at an edge. However, the cases of single-edge fixed delays of duration \(\tau \) rounds in single-source bipartite graphs terminate by round \(2d+\tau -1\), and all cases of multiple-edge fixed delays in multiple-source cycles terminate.

我们考虑了有状态分布式网络泛洪算法的无状态“健忘症”变体，扩展了我们的会议论文 [PODC'19，STACS'20]。泛洪开始于一组源“初始”节点，我试图在一个由一组节点G和边E的无向图 ( G ,  E ) 表示的网络中轮流广播消息M。在每一轮中，具有M的节点将M发送给所有在上一轮中未从其接收到M的邻居。节点不记得前几轮，提高了M无限循环。状态泛洪通过节点记录每条传播的消息并在再次收到时忽略M来克服这个问题。这种开销被认为是必要的。我们表明，即使没有这种开销，仍然可以实现几乎最佳的广播。我们证明健忘症泛洪在每个有限图上终止，并得出终止时间的明确界限。如果将I 中的所有节点收缩到单个节点的商图是二分的，则将( G ,  E ) 定义为I-二分。我们证明，如果d是直径并且e ( I ) 是集合I的偏心率，则泛洪终止于e( I ) 舍入如果 ( G ,  E ) 是 I-bipartite 且j舍入e ( I ) < j \(\le \) \(e(I)+d+1 \le 2d +1\) if ( G ,  E ) 是非 I-二部的。终止时间的分离可用于图形中拓扑/距离的分布式发现。如果边缘在泛洪过程中丢失，则可以保证终止，但通常情况下，如果边缘存在延迟，则不会终止。然而，单源二分图中持续时间为\(\tau \)轮的单边固定延迟的情况以轮\(2d+\tau -1\)终止，并且多源循环中的多边固定延迟的所有情况都终止。