Lecture Notes in Computer Science 4917

378 C.–C. Lin and C.–L. Chen
� Si – the code size of bytecode handler Vi.
� N – the size of one NAND flash page.
� M(Pk ) – the size of partition Pk. It is ΣSm for all Vm∈ Pk .
� H(Pk ) – the value of partition Pk. It is ΣFi,j for all Vi , Vj ∈ Pk .
Our goal was to construct partitions that satisfy the following constrains.
Definition 2. The problem is to divide G into K disjoined partitions {P1, P2,…,Pk}.
For each Pk that M(Pk) ≤ N. Such that Wi,j is minimized. And maximize ΣH(Pi ) for all
Pi ∈ {P1, P2,…,Pk}.
This rectified model is exactly an application of the graph partition problem, i.e., the
size of each partition must satisfy the constraint (NAND flash page size), and the sum
of intra-partition path weights is minimal. The graph partition problem is NPcomplete
[13]. However, the purpose of this paper was neither to create a new graph
partition algorithm nor to discuss difference between existing algorithms. The
experimental implementation just adopted the following algorithm to demonstrate our
approach works. Other implementations based on this approach may choose another
graph partition algorithm that satisfies specific requirements.
Partition (G)
1. Find the edge with maximal weight Fi,j among graph G, while the Si + Sj ≤ N.
If there is no such an edge, go to step 4.
2. Call Merge (Vi, Vj ) to combine vertexes Vi and Vj.
3. Remove both Vi and Vj from G. go to step 1.
4. Find a pair of vertexes Vi and Vj in G such that Si + Sj ≤ N. If there isn’t a pair
satisfied the criteria, go to step 7.
5. Call Merge (Vi , Vj ) to combine vertexes Vi and Vj.
6. Remove both Vi and Vj out of G. go to step 4.
7. End.
The procedure of merging both vertexes Vi and Vj is:
Merge (Vi , Vj )
1. Add a new vertex Vk. to G.
2. Pickup an edge E connects Vt with either Vi or Vj. If there is no such an edge,
then go to step 6.
3. If there is already an edge F connects Vt to Vk,
4. Then, add the weight of E to F, and discard E.
5. Else, replace one end of E which is either Vi or Vj with Vk.
6. End.
Finally, each vertex in G is an aggregation of several bytecode handlers. The
refinement process is to collect bytecode handlers belong to the same vertex and place
them into one NAND flash page.
5 Refinement Process
The implementation of the refinement process consisted of two steps. The refinement
process acted as a post processor of the compiler. It parsed intermediate files