Algorithm 1. HECRA

Input: node ID, initial energy, depth

Output: Cluster results

State 1: Network Initialization

For each node i

Broadcast HELLO = {node ID}

If receive HELLO

$N{e}_i=N{e}_i+1$

End If

End For

State 2: Cluster head selection and cluster formation

For each node i

Calculate weight $T_i^{’}$ as in (9)

Generate a random number $0\le rand\le 1$

If $rand<T_i^{’}$

Elect node i to become CH

Else if receive Cluster formation message

Calculate weight $H_j$ as in (10)

Join the cluster corresponding to the CH $H_j$

Else

Node goes to sleep

End If

End For

State 3: Data transmission

For all CHs

Collecting and fusing information from nodes in the cluster

Broadcast wayfinding message

If receive wayfinding message

Determines whether to reply to the sender of wayfinding message

End If

If receive messages of confirmation

Calculate weight ${\omega }_i$ as in (11)

Find the node that forwarded the message

End If

End For

State 4: Optimization of the network

AUV seeks CHs that are unable to communicate with other nodes

Find the location of the relay transmission

Assisted in completing data forwarding and continued cruising