Multiple sequence alignment is a fundamental problem in computational biology. Because of its notorious difficulties, aligning sequences within a constant band (c-diagonal) is a popular practice in bioinformatics with good practical results [D. Sankoff, J. Kruskal, Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison–Wesley, 1983; W.R. Pearson, D. Lipman, Improved tools for biological sequence comparison, Proc. Natl. Acad. Sci. USA 85 (1988) 2444– 2448; W.R. Pearson, Rapid and sensitive sequence comparison with FASTP and FASTA, Methods Enzymol. 183 (1990) 63–98; W.R. Pearson, Searching protein sequence libraries: Comparison of the sensitivity and selectivity of the Smith–Waterman and FASTA algorithms, Genomics 11 (1991) 635–650; S. Altschul, D. Lipman, Trees, stars, and multiple sequence alignment, SIAM J. Appl. Math. 49 (1989) 197–209; K. Chao, W.R. Pearson, W. Miller, Aligning two sequences within a specified diagonal ba...