For the purpose of extending the lifetime of wireless sensor networks (WSNs)

this paper proposes a Topology Construction with the Optimal Resilience (TC-OR) algorithm

which is used to construct a virtual backbone based on regular tree.Firstly

nodes with more energy and higher degree are chosen as the nodes of the regular tree;secondly

in order to build the links of the tree

some nodes are picked out as supplemental nodes;then Annealing is used with a function of evaluation to confirm the exact positions of the tree nodes and the supplemental nodes;finally the virtual backbone networks with a optimal resilience is established.The simulation results demonstrate that the proposed algorithms can effectively improve the resilience of the virtual backbone networks

as a result to prolong network lifetime

and to perform better in small and medium sized WSNs.