Adaptive Fault-Tolerant Routing in 2D Mesh with Cracky Rectangular Model

Table 2

The routing table for border nodes of cracky blocks.

	𝑣's border position is west		𝑣's border position is east
𝑣𝑝=𝑊(𝑣)	(𝑣𝑠←𝐸(𝑣) and succ1(𝑣)←𝑁(𝑣)) if (a)		𝑣𝑠←succ1(𝑣)
	𝑣𝑠←𝑁(𝑣) if (b)
𝑣𝑝=𝑆(𝑣)	(𝑣𝑠←𝐸(𝑣) and succ1(𝑣)←𝑁(𝑣)) if (a)		(𝑣𝑠←𝑊(𝑣) and succ1(𝑣)←𝑁(𝑣)) if (a)
	𝑣𝑠←𝑁(𝑣) if (b)		𝑣𝑠←𝑁(𝑣) if (b)
𝑣𝑝=𝐸(𝑣)	𝑣𝑠←succ1(𝑣)		(𝑣𝑠←𝑊(𝑣) and succ1(𝑣)←𝑆(𝑣)) if (a)
			𝑣𝑠←𝑆(𝑣) if (b)
𝑣𝑝=𝑁(𝑣)	(𝑣𝑠←𝐸(𝑣) and succ1(𝑣)←𝑆(𝑣)) if (a)		(𝑣𝑠←𝑊(𝑣) and succ1(𝑣)←𝑆(𝑣)) if (a)
	𝑣𝑠←𝑆(𝑣) if (b)		𝑣𝑠←𝑆(𝑣) if (b)
	𝑣's border position is south		𝑣's border position is north
𝑣𝑝=𝑊(𝑣)	(𝑣𝑠←𝑁(𝑣) and succ1(𝑣)←𝐸(𝑣)) if (a)		(𝑣𝑠←𝑆(𝑣) and succ1(𝑣)←𝐸(𝑣)) if (a)
	𝑣𝑠←𝐸(𝑣) if (b)		𝑣𝑠←𝐸(𝑣) if (b)
𝑣𝑝=𝑆(𝑣)	(𝑣𝑠←𝑁(𝑣) and succ1(𝑣)←𝑊(𝑣)) if (a)		𝑣𝑠←succ1(𝑣)
	𝑣𝑠←𝑊(𝑣) if (b)
𝑣𝑝=𝐸(𝑣)	(𝑣𝑠←𝑁(𝑣) and succ1(𝑣)←𝑊(𝑣)) if (a)		(𝑣𝑠←𝑆(𝑣) and succ1(𝑣)←𝑊(𝑣)) if (a)
	𝑣𝑠←𝑊(𝑣) if (b)		𝑣𝑠←𝑊(𝑣) if (b)
𝑣𝑝=𝑁(𝑣)	𝑣𝑠←succ1(𝑣)		(𝑣𝑠←𝑆(𝑣) and succ1(𝑣)←𝐸(𝑣)) if (a)
			𝑣𝑠←𝐸(𝑣) if (b)
	𝑣's border position is NE corner	𝑣's border position is SE corner	𝑣's border position is SW corner	𝑣's border position is NW corner
𝑣𝑝=𝑊(𝑣)	𝑣𝑠←𝑣𝑖 if (c)	𝑣𝑠←𝑣𝑖 if (c)	(d)	(d)
	𝑣𝑠←𝑆(𝑣)	𝑣𝑠←𝑁(𝑣)
𝑣𝑝=𝑆(𝑣)	𝑣𝑠←𝑣𝑖 if (c)	(d)	(d)	𝑣𝑠←𝑣𝑖 if (c)
	𝑣𝑠←𝑊(𝑣)			𝑣𝑠←𝐸(𝑣)
𝑣𝑝=𝐸(𝑣)	(d)	(d)	𝑣𝑠←𝑣𝑖 if (c)	𝑣𝑠←𝑣𝑖 if (c)
			𝑣𝑠←𝑁(𝑣)	𝑣𝑠←𝑆(𝑣)
𝑣𝑝=𝑁(𝑣)	(d)	𝑣𝑠←𝑣𝑖 if (c)	𝑣𝑠←𝑣𝑖 if (c)	(d)
		𝑣𝑠←𝑊(𝑣)	𝑣𝑠←𝐸(𝑣)

(a): is not final.
(b): is final.
(c): let the destination node of the message be 𝑌, if ∃𝑣_𝑖∈Γ(𝑣) and 𝑣_𝑖's status is good, s.t. 𝑑(𝑣_𝑖,𝑌)=𝑑(𝑣,𝑌)−1.
(d): using the basic routing function.