Sequence allignment The optimum cost of an alignment of the strings x1 x2 x3 x4

Question

Sequence allignment

The optimum cost of an alignment of the strings

x1 x2 x3 x4 ... x_m and y1 y2 y3 ... y_n

will always be greater than the optimum cost of an alignment of

   x2 x3 x4 ... x_m and y1 y2 y3 ... y_n

because any alignment of the first pair of strings necessarily contains an alignment of the second pair of strings.

This is NOT correct!

It is NOT true that any alignment of the first pair of strings necessarily contains an alignment of the second pair of strings: For example, let x = CT and let y = CG. It is NOT true that any alignment of these start with x1 = C against a gap, followed by an alignment of x2 against y1 y2 (i.e., an alignment of T against CG). Here is such an alignment:

A T
A G

This alignment has cost 1, whereas any alignment that starts with the first A in x against a gap necessarily will have cost at least 2 for that first gap, and optimally has cost 5:

A T -
- A G

Is it possible to have a situation in table "opt" where x_i is the same character as y_j and have

opt[ i ][ j ] = 2 + opt[ i+1][ j ] = 2 + opt[ i ][ j+1]    = 0 + opt[ i + 1][ j + 1]

(In other words, when creating the alignment, we could have come from ANY of the 3 neighboring squares below and to the right?

You need to compute the entire "opt" table, and see if there exists an i and a j such that x_i == y_j and when you are computing the value of opt[i][j], it is a 3-way tie between 2+opt[i + 1][j], 2+opt[i][j + 1], and opt[i+1][j+1].

Explanation / Answer

ecture Notes in Computer Science 1547 Edited by G. Goos, J. Hartmanis and J. van Leeuwen 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Sue H. Whitesides (Ed.) Graph Drawing 6th International Symposium, GD ’98 Montreal, Canada, August 13-15, 1998 Proceedings 1 3 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editor Sue H. Whitesides School of Computer Science, McGill University 3480 University St. #318, Montreal, Quebec H3A 2A7, Canada E-mail: sue@cs.mcgill.ca Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Graph drawing : 6th international symposium ; proceedings / GD ’98, Montreal, Canada, August 13 - 15, 1998. Sue H. Whitesides (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 1999 (Lecture notes in computer science ; Vol. 1547) ISBN 3-540-65473-9 CR Subject Classification (1998): I.4, I.2.9-10, I.3.1, C.3 ISSN 0302-9743 ISBN 3-540-65473-9 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, a ecture Notes in Computer Science 1547 Edited by G. Goos, J. Hartmanis and J. van Leeuwen 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Sue H. Whitesides (Ed.) Graph Drawing 6th International Symposium, GD ’98 Montreal, Canada, August 13-15, 1998 Proceedings 1 3 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editor Sue H. Whitesides School of Computer Science, McGill University 3480 University St. #318, Montreal, Quebec H3A 2A7, Canada E-mail: sue@cs.mcgill.ca Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Graph drawing : 6th international symposium ; proceedings / GD ’98, Montreal, Canada, August 13 - 15, 1998. Sue H. Whitesides (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 1999 (Lecture notes in computer science ; Vol. 1547) ISBN 3-540-65473-9 CR Subject Classification (1998): I.4, I.2.9-10, I.3.1, C.3 ISSN 0302-9743 ISBN 3-540-65473-9 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, a

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