TY - JOUR

T1 - Sequential and Parallel Approximation of Shortest Superstrings

AU - Czumaj, Artur

AU - Ga̧sieniec, Leszek

AU - Piotrów, Marek

AU - Rytter, Wojciech

N1 - Funding Information:
Superstrings have many applications in data compression and genetics. However, the decision version of the shortest superstring problem is N P-complete. In this paper we examine the complexity of approximating shortest superstrings. There are two basic measures of the approximations: the length factor and the compression factor. The well known and practical approximation algorithm is the sequential algorithm GREEDY. It approximates the shortest superstring with the compression factor of 21 and with the length factor of 4. Our main results are: 1) A sequential length approximation algorithm which achieves a length factor of 2.83. This result improves the best previously known bound of 2.89 due to Teng and Yao. Very recently, this bound was improved by Kosaraju, Park, and Stein to 2.79, and by Armen and Stein to 2.75. 2) A proof that the algorithm GREEDY is not paralleliz- * Supported by DFG-Graduiertenkolleg ``Parallele Rechnernetzwerke in der Produktion-stechnik,'' ME 872r4-1 and by the ESPRIT Basic Research Action No. 7141 ALCOM II). E-mail: artur@uni-paderborn.de. ² Work done while visiting University of Paderborn, supported by Alexander von Humboldt Stiftung. Supported also in part by Volkswagen Stiftung, by Grant No. KBN 2 P301 034 07, and by ESPRIT Basic Research Action No. 7141 ALCOM II). ³Supported by Grant No. KBN 8I11 C01208.

PY - 1997/4

Y1 - 1997/4

N2 - Superstrings have many applications in data compression and genetics. However, the decision version of the shortest superstring problem is script N sign℘-complete. In this paper we examine the complexity of approximating shortest superstrings. There are two basic measures of the approximations: the length factor and the compression factor. The well known and practical approximation algorithm is the sequential algorithm GREEDY. It approximates the shortest superstring with the compression factor of 1/2 and with the length factor of 4. Our main results are: (1) A sequential length approximation algorithm which achieves a length factor of 2.83. This result improves the best previously known bound of 2.89 due to Teng and Yao. Very recently, this bound was improved by Kosaraju, Park, and Stein to 2.79, and by Armen and Stein to 2.75. (2) A proof that the algorithm GREEDY is not parallelizable, the computation of its output is ℘-complete. (3) An script N signscript C sign algorithm which achieves the compression factor of 1/(4 + ε). (4) The design of an ℛscript N signscript C sign algorithm with constant length factor and an script N signscript C sign algorithm with logarithmic length factor.

AB - Superstrings have many applications in data compression and genetics. However, the decision version of the shortest superstring problem is script N sign℘-complete. In this paper we examine the complexity of approximating shortest superstrings. There are two basic measures of the approximations: the length factor and the compression factor. The well known and practical approximation algorithm is the sequential algorithm GREEDY. It approximates the shortest superstring with the compression factor of 1/2 and with the length factor of 4. Our main results are: (1) A sequential length approximation algorithm which achieves a length factor of 2.83. This result improves the best previously known bound of 2.89 due to Teng and Yao. Very recently, this bound was improved by Kosaraju, Park, and Stein to 2.79, and by Armen and Stein to 2.75. (2) A proof that the algorithm GREEDY is not parallelizable, the computation of its output is ℘-complete. (3) An script N signscript C sign algorithm which achieves the compression factor of 1/(4 + ε). (4) The design of an ℛscript N signscript C sign algorithm with constant length factor and an script N signscript C sign algorithm with logarithmic length factor.

UR - http://www.scopus.com/inward/record.url?scp=0347933676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347933676&partnerID=8YFLogxK

U2 - 10.1006/jagm.1996.0823

DO - 10.1006/jagm.1996.0823

M3 - Article

AN - SCOPUS:0347933676

SN - 0196-6774

VL - 23

SP - 74

EP - 100

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 1

ER -