Minimal Sets of Turns for Breaking Cycles in Graphs Modeling Networks

Abstract

The problem of preventing deadlocks and livelocks in computer communication networks, in particular, those with wormhole routing, is considered. The method to prevent deadlocks is to prohibit certain turns (i.e., the use of certain pairs of connected edges) in the routing process, in such a way that eliminates all cycles in the graph. We propose a new algorithm that constructs a minimal (irreducible) set of turns that breaks all cycles and preserves connectivity of the graph. The algorithm is tree-free and is considerably simpler than earlier cycle-breaking algorithms. We prove its properties and present lower and upper bounds for minimum cardinalities of cycle-breaking connectivity preserving sets for graphs of general topology as well as for planar graphs. In particular, the algorithm guarantees that not more than 1=3 of all turns in the network become prohibited. We also present experimental results on the fraction of prohibited turns, the distance dilation, as well as on the message delivery times and saturation loads for the proposed algorithm in comparison with known tree-based algorithms. The proposed algorithm outperforms substantially the tree-based algorithms in all characteristics considered.

Wireless Resilient Routing Reconfiguration

“…Though this problem is irksome, it is not critical: auxiliary techniques (e.g., forwarding only once, flow decomposition, or prohibiting turns [6]) can ameliorate it, and like the reconfiguration as a whole, it is a transient issue that lasts only until a new base routing can be solved for. It is also plausible that additional constraints along the lines of r ab ( ) = r a b ( ) might circumvent the problem altogether.…”

An Analytical Model for Virtual Cut-Through Routing

“…Various routing techniques are used in interconnection networks (e.g., [2][3][4][5][6][7][8][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). Store-and-forward approach is based on the assumption that an entire message must be received at any intermediate node before it can be forwarded to the next node.…”

“…This forms a long "worm" which remains in the network blocking other messages, thereby increasing their delivery time. Also, the problem of deadlocks emerges in this approach and should be dealt with (e.g., [21][22][23][24]).…”

Simulation Study of Interconnection Networks with Virtual Cut-through Routing

“…This forms a long "worm" which remains in the network blocking other messages, thereby increasing their delivery time. Also, the problem of deadlocks emerges in this approach and should be dealt with (Levitin, Karpovsky, and Mustafa 2009;Karpovsky, Levitin, and Mustafa 2014).…”