b'@techreport{BreslauerJiangZhigen97,'b'\nTITLE = {Rotations of periodic strings and short superstrings},\nAUTHOR = {Breslauer, Dany and Jiang, Tao and Jiang, Zhigen},\nLANGUAGE = {eng},\nNUMBER = {MPI-I-1996-1-019},\nINSTITUTION = {Max-Planck-Institut f{\\"u}r Informatik},\nADDRESS = {Saarbr{\\"u}cken},\nYEAR = {1996},\nDATE = {1996},\nABSTRACT = {This paper presents two simple approximation algorithms for the shortest superstring problem, with approximation ratios $2 {2\\over 3}$ ($\\approx 2.67$) and $2 {25\\over 42}$ ($\\approx 2.596$), improving the best previously published $2 {3\\over 4}$ approximation. The framework of our improved algorithms is similar to that of previous algorithms in the sense that they construct a superstring by computing some optimal cycle covers on the distance graph of the given strings, and then break and merge the cycles to finally obtain a Hamiltonian path, but we make use of new bounds on the overlap between two strings. We prove that for each periodic semi-infinite string $\\alpha = a_1 a_2 \\cdots$ of period $q$, there exists an integer $k$, such that for {\\em any} (finite) string $s$ of period $p$ which is {\\em inequivalent} to $\\alpha$, the overlap between $s$ and the {\\em rotation} $\\alpha[k] = a_k a_{k+1} \\cdots$ is at most $p+{1\\over 2}q$. Moreover, if $p \\leq q$, then the overlap between $s$ and $\\alpha[k]$ is not larger than ${2\\over 3}(p+q)$. In the previous shortest superstring algorithms $p+q$ was used as the standard bound on overlap between two strings with periods $p$ and $q$.},\nTYPE = {Research Report / Max-Planck-Institut f\xc3\xbcr Informatik},\n}\n'