Algorithm 1 ABIDE Algorithm.

message formats: Forward(message type, sender, parent, list), Backward(message type, sender, destination, cycleID)

initially: id is the unique node identifier; visited←false; cycleID←null; parent←null; backwardCount←childCount←0; cycleIDset←ancestors←∅

sink node multicasts Forward(forward type,sink,null,null) to neighbors

upon a node receives a message

if msg.type = Forward then call ReceiveForward(msg)

else if msg.type = Backward then call ReceiveBackward(msg) end if

end upon

procedure ReceiveForward(Message msg)

if visited = false then

visited←true; parent←msg.sender; ancestors←msg.ancestors; ancestors.append(parent)

multicast Forward(forward type,id,parent,ancestors); start BackwardTimer

else

if msg.parent = id then childCount←childCount+1

else cycleIDset.add(ancestors⋏msg.ancestors); mark the link to msg.sender as non-bridge

end if

end if

end procedure

upon BackwardTimer expires

if childCount = 0 and id≠sink then call SendBackward() end if

end upon

procedure SendBackward()

if cycleIDset is empty then

mark the link to parent as bridge; send Backward(backward_type,id,parent,null) to parent

else

mark the link to parent as non-bridge; cycleID ←front(ancestors,cycleIDset)

send Backward(backward type,id,parent,cycleID) to parent

end if

end procedure

procedure ReceiveBackward(Message msg)

backwardCount←backwardCount+1

if msg.cycleID = null then mark the link to msg.sender as bridge

else

mark the link to msg.sender as non-bridge

if msg.cycleID≠id then cycleIDset.add(msg.cycleID) end if

end if

if backwardCount = childCount then call sendBackward() end if

end procedure