TY - JOUR

T1 - An asynchronous self-stabilizing approximation for the minimum CDS with safe convergence in UDGs

AU - Kamei, Sayaka

AU - Izumi, Tomoko

AU - Yamauchi, Yukiko

N1 - Funding Information:
This work was supported in part by KAKENHI Nos. 26330015 and 15K15938 .

PY - 2016/2/15

Y1 - 2016/2/15

N2 - A connected dominating set (CDS) is useful in forming a virtual backbone in wireless ad hoc or sensor networks because these networks lack a fixed infrastructure and centralized management. Self-stabilization guarantees that the system tolerates any finite number of transient faults and does not need any initialization. The safe convergence property guarantees that the system quickly converges to a feasible safe configuration, and subsequently converges to a legitimate configuration without violating safety. A previous publication on a safely converging algorithm for the minimum CDS assumed a phase clock synchronizer, which is a very strong assumption. In this paper, we propose the first asynchronous self-stabilizing (6+ε)-approximation algorithm with safe convergence for the minimum CDS in networks modeled by unit disk graphs (UDGs). We assume that the feasible safe configuration satisfies the condition that a dominating set is constructed. The convergence time to a feasible safe configuration is one round, and the convergence time to a legitimate configuration in which an approximated minimum CDS is constructed is O(max{d2, n}) rounds, and O(n6) steps.

AB - A connected dominating set (CDS) is useful in forming a virtual backbone in wireless ad hoc or sensor networks because these networks lack a fixed infrastructure and centralized management. Self-stabilization guarantees that the system tolerates any finite number of transient faults and does not need any initialization. The safe convergence property guarantees that the system quickly converges to a feasible safe configuration, and subsequently converges to a legitimate configuration without violating safety. A previous publication on a safely converging algorithm for the minimum CDS assumed a phase clock synchronizer, which is a very strong assumption. In this paper, we propose the first asynchronous self-stabilizing (6+ε)-approximation algorithm with safe convergence for the minimum CDS in networks modeled by unit disk graphs (UDGs). We assume that the feasible safe configuration satisfies the condition that a dominating set is constructed. The convergence time to a feasible safe configuration is one round, and the convergence time to a legitimate configuration in which an approximated minimum CDS is constructed is O(max{d2, n}) rounds, and O(n6) steps.

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U2 - 10.1016/j.tcs.2015.12.001

DO - 10.1016/j.tcs.2015.12.001

M3 - Article

AN - SCOPUS:84953291227

VL - 615

SP - 102

EP - 119

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -