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courses:cs211:winter2011:journals:charles:chapter6 [2011/03/30 03:45] – [6.7 Sequence Alignment in Linear Space via Divide and Conquer] gouldc | courses:cs211:winter2011:journals:charles:chapter6 [2011/04/05 05:52] (current) – [6.9 Shortest Paths and Distance Vector Protocols] gouldc | ||
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This section shows us an improved algorithm for sequence alignment. It still runs in O(mn) time but it decreases the space requirement from O(mn) to O(m+n). We realize that computing a single column in the memoized array in the last problem only requires us to know about the current column and the previous column. Therefore it is possible to arrive at the solution while only maintaining a m-by-2 array instead of a m-by-n array. This idea will work nicely for building up to the solution //value// (i.e., the total cost of all gaps and mismatches)... but we also want to know the optimal // | This section shows us an improved algorithm for sequence alignment. It still runs in O(mn) time but it decreases the space requirement from O(mn) to O(m+n). We realize that computing a single column in the memoized array in the last problem only requires us to know about the current column and the previous column. Therefore it is possible to arrive at the solution while only maintaining a m-by-2 array instead of a m-by-n array. This idea will work nicely for building up to the solution //value// (i.e., the total cost of all gaps and mismatches)... but we also want to know the optimal // | ||
- | I am having a difficult time wrapping my head around | + | We do this by incorporating divide-and-conquer principles into our algorithm. |
===== 6.8 Shortest Paths in a Graph ===== | ===== 6.8 Shortest Paths in a Graph ===== | ||
+ | Problem outline: We want to find the shortest path between two nodes in a directed graph. We cannot use Dijkstra' | ||
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+ | Here we assume no negative cycles because otherwise the optimal path would follow that cycle infinitely many times and so reduce the cost of the path to negative infinity. But that would be stupid. We saw from class that like the problem above we can fill any column by referring only to the column itself and the column that came before it. | ||
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+ | (6.25) says that the shortest path algorithm can run in O(mn) time. | ||
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+ | ===== 6.9 Shortest Paths and Distance Vector Protocols ===== | ||
+ | Outline: An instance of the shortest-path problem on an undirected graph for which all edge costs are positive. Dijkstra' | ||
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+ | Problems: Assumes edge costs will remain constant during runtime, which for many reasons will probably not be the case in practice. Also, there is the potential " |