To cope with the constraint problem of power consumption and transmission delay in the virtual backbone of wireless sensor network, a distributed connected dominating set （CDS） algorithm with （α,β）-constraints is proposed. Based on the （α, β）-tree concept, a new connected dominating tree with bounded transmission delay problem（CDTT） is defined and a corresponding algorithm is designed to construct a CDT-tree which can trade off limited total power and bounded transmission delay from source to destination nodes. The CDT algorithm consists of two phases： The first phase constructs a maximum independent set（MIS）in a unit disk graph model. The second phase estimates the distance and calculates the transmission power to construct a spanning tree in an undirected graph with different weights for MST and SPF, respectively. The theoretical analysis and simulation results show that the CDT algorithm gives a correct solution to the CDTF problem and forms a virtual backbone with（ α,β）-constraints balancing the requirements of power consumption and transmission delay.
