Map Quality

We have used several criteria to quantify the quality of the constructed map. The major criteria included the presence of unacceptable big errors in the constructed map, the average size of errors between consecutive clones, and the number of breakpoints in the clone-order permutation. We detail how to evaluate the map quality. We measure the distance between clones a,b as the number of left clone endpoints between the left endpoints of a and b. Using the order of the left endpoints of clones in the constructed map, we compute the distance d₁ between consecutive clones and compare it with the distance d₂ between the same two clones in the correct map (note that the two clones need not necessarily be consecutive or even close in the correct map). If the difference |d₁ - d₂| is more than a clone's length, we call it a big error (see Figure 9.11). Otherwise, it is called a small error. The average of the small errors is also calculated and is called the average error. As it is possible that the constructed map is oriented in the reverse direction with respect to the correct one, we repeat the calculation with reversed orientations. The correct orientation is assumed to have a longer clone sequence with no big errors. In case this is not a sufficient criterion (there are no big errors in both orientations, or the first error in both orientations occurs after the same number of clones) we choose the orientation minimizing average error. We then advance to the location of the first big error and select the orientation for the rest of the mapping using the same considerations we used for the first one. This procedure is repeated till the whole map was traversed. A 0 or 1 variable any big is defined to be a 1 if the constructed map contains at least one big error. Its average over a number of simulations is used to estimate the probability of a constructed map to contain big errors.

  

Figure 9.11: A big error in a constructed map. The difference between the actual distance between the two clones and the distance on the map is bigger than the avergae length of a clone.