| Ad hoc network normally has critical connectivity properties before partitioning. The timely recognition is important in order to perform some data or service replication. Several existing centralized or globalized algorithms declare an edge or a node as critical if their removal will separate the network into several components. We introduce several localized definitions of critical nodes and critical links, using topological or positional information. A node is critical if the subgraph of k-hop neighbours of node (without the node itself) is disconnected. We propose three definitions of critical links, based on verifying common k-hop neighbours, loop length, and critical status of link endpoints, respectively. The experiments with random unit graph model of ad hoc networks show high correspondence of local and global decisions. For instance, in experiments with 500 nodes in connected random unit graphs, over half of locally estimated critical nodes and links were indeed globally critical even for k=1 (the accuracy increases to over 70% for k=2 and over 80% for k=3), for average number of neighbours ranging from 3 to 15. The errors mostly occur when alternative routes exist but are relatively long, and therefore may not provide satisfactory service in applications. Therefore our localized protocols provide faster and often more reliable partition warnings for possible timely replication decisions. |
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