The Construction Algorithm

1.

Initialize a collection of contigs, each of which is a set of clones. Initially, the collection includes for each clone, a contig consisting of that clone.

2.

Calculate P_x,y[t] for each $x,y \in \{0,1\}$ and for each representative t in [0,l].

3.

Calculate |S_x,y(a,b)| for each pair a,b of contigs and foreach $x,y \in \{0,1\}$.

4.

Calculate for all the initial contig pairs and for the two possible relative orientations their relative placement probabilities vector. The results are stored in a table.

5.

Find for all contig pairs and for their two possible relative orientations their best relative placement, and its probability.

6.

While more than one contig remains:
(a) Find two contigs a,b which have relative orientation and placement that attain the highest probability.
(b) Merge b into a.
(c) Change the table calculated in step 4 to reflect the last merge. Only the table entries for all contig pairs (a,c) need to be changed. The required change is a simple combination of the previous entries for (a,c) and for (b,c).
(d) Find, for contig pairs affected by the merge, their new best relative placement.

Assume that there are n probes and m clones of length d, and the genome has length L. The bottleneck steps in the computation are:

• Steps 2-3 that takes O(m²n) time.
• Steps 4-5 that take O(m²d) time
• Steps 6(c) and 6(d) that take O(mL) time.

Step 6 is repeated m-1 times thus the total complexity of the algorithm is O(m²(L+d+n)).