Authenticated Location-Aware Publish/Subscribe Services in Untrusted Outsourced Environments

Algorithm 1

Filter-verification framework with inverted index pruning.

Input: TMR-tree: the text-aware Merkle R-tree on messages within ; : the inverted index of spatial-oriented prefixes

Output: : answers of each message in the TMR-tree

(1) TMR-tree.Root.;

(2) Initialize Stack ;

(3) .Push(TMR-tree.Root);

(4) while   is not empty do

(5).Pop();

(6)for each    do

(7)for each    do

(8)if    then

(9).Add();

(10)if    and   is not a message  then

(11).Push(.children);

(12) for  each  do

(13)for  each    do

(14)if  Verify()  then

(15).Add();

(16) return ;