Deadlock-free routing in arbitrary networks via the flattest common supersequence method
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
An approximation algorithm for the shortest common supersequence problem: an experimental analysis
Proceedings of the 2001 ACM symposium on Applied computing
Approximation algorithms for the shortest common supersequence
Nordic Journal of Computing
An approximate A* algorithm and its application to the SCS problem
Theoretical Computer Science
On the complexity of finding common approximate substrings
Theoretical Computer Science
Common Subsequences and Supersequences and their Expected Length
Combinatorics, Probability and Computing
A learning algorithm for the longest common subsequence problem
Journal of Experimental Algorithmics (JEA)
Combined super-/substring and super-/subsequence problems
Theoretical Computer Science
On the complexity of finding emerging patterns
Theoretical Computer Science - Pattern discovery in the post genome
Fast and accurate algorithms for protein side-chain packing
Journal of the ACM (JACM)
Communication: A note on the precedence-constrained class sequencing problem
Discrete Applied Mathematics
Longest common subsequence problem for unoriented and cyclic strings
Theoretical Computer Science
An adaptive branch and bound approach for transforming job shops into flow shops
Computers and Industrial Engineering
Exemplar Longest Common Subsequence
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New efficient algorithms for the LCS and constrained LCS problems
Information Processing Letters
Finding the longest common subsequence for multiple biological sequences by ant colony optimization
Computers and Operations Research
Algorithms for computing variants of the longest common subsequence problem
Theoretical Computer Science
A New Efficient Algorithm for Computing the Longest Common Subsequence
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
On the Longest Common Parameterized Subsequence
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence
Improved bounds on the average length of longest common subsequences
Journal of the ACM (JACM)
On the approximability of the Maximum Agreement SubTree and Maximum Compatible Tree problems
Discrete Applied Mathematics
Beam search for the longest common subsequence problem
Computers and Operations Research
Maximum Motif Problem in Vertex-Colored Graphs
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Improved Approximation Results on the Shortest Common Supersequence Problem
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
On the longest common parameterized subsequence
Theoretical Computer Science
Finite automata based algorithms on subsequences and supersequences of degenerate strings
Journal of Discrete Algorithms
The longest haplotype reconstruction problem revisited
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Efficient stochastic local search algorithm for solving the shortest common supersequence problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Computational Biology and Chemistry
Variants of constrained longest common subsequence
Information Processing Letters
The complexity of flood filling games
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Complexity issues in vertex-colored graph pattern matching
Journal of Discrete Algorithms
Approximating minimum reset sequences
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Evolutionary-based iterative local search algorithm for the shortest common supersequence problem
Proceedings of the 13th annual conference on Genetic and evolutionary computation
An improved algorithm for the longest common subsequence problem
Computers and Operations Research
Restricted common superstring and restricted common supersequence
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Weighted shortest common supersequence
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
The multiple sequence sets: problem and heuristic algorithms
Journal of Combinatorial Optimization
RNA multiple structural alignment with longest common subsequences
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On the approximation of computing evolutionary trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Optimizing monitoring queries over distributed data
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
Lower bounds and parameterized approach for longest common subsequence
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
On the parameterized complexity of the repetition free longest common subsequence problem
Information Processing Letters
On the longest common rigid subsequence problem
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Explicit inapproximability bounds for the shortest superstring problem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
An enhanced beam search algorithm for the Shortest Common Supersequence Problem
Engineering Applications of Artificial Intelligence
A hyper-heuristic for the Longest Common Subsequence problem
Computational Biology and Chemistry
Approximability of constrained LCS
Journal of Computer and System Sciences
New results for the Longest Haplotype Reconstruction problem
Discrete Applied Mathematics
Exemplar longest common subsequence
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Hardness of longest common subsequence for sequences with bounded run-lengths
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Algorithms for computing the longest parameterized common subsequence
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
The constrained shortest common supersequence problem
Journal of Discrete Algorithms
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The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) are two well-known {\bf NP}-hard problems that have applications in many areas including computational molecular biology, data compression, robot motion planning and scheduling, text editing, etc. A lot of fruitless effort has been spent in searching for good approximation algorithms for these problems. In this paper, we show that these problems are inherently hard to approximate in the worst case. In particular, we prove that (i) SCS does not have a polynomial time linear approximation algorithm, unless {\bf P} = {\bf NP}; (ii) There exists a constant $\delta 0$ such that, if SCS has a polynomial time approximation algorithm with ratio $\log^{\delta} n$, where $n$ is the number of input sequences, then {\bf NP} is contained in {\bf DTIME}$(2^{\polylog n})$; (iii) There exists a constant $\delta 0$ such that, if LCS has a polynomial time approximation algorithm with performance ratio $n^{\delta}$, then {\bf P} = {\bf NP}. The proofs utilize the recent results of Arora et al. [Proc. 23rd IEEE Symposium on Foundations of Computer Science, 1992, pp. 14-23] on the complexity of approximation problems. In the second part of the paper, we introduce a new method for analyzing the average-case performance of algorithms for sequences, based on Kolmogorov complexity. Despite the above nonapproximability results, we show that near optimal solutions for both SCS and LCS can be found on the average. More precisely, consider a fixed alphabet $\Sigma$ and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length $n$. Moreover, assume that the number of input sequences is polynomial in $n$. Then, there are simple greedy algorithms which approximate SCS and LCS with expected additive errors $O(n^{0.707})$ and $O(n^{\frac{1}{2}+\epsilon})$ for any $\epsilon 0$, respectively. Incidentally, our analyses also provide tight upper and lower bounds on the expected LCS and SCS lengths for a set of random sequences, solving a generalization of another well-known open question on the expected LCS length for two random sequences [K. Alexander, The rate of convergence of the mean length of the longest common subsequence, 1992, manuscript],[V. Chvatal and D. Sankoff, J. Appl. Probab., 12 (1975), pp. 306-315], [D. Sankoff and J. Kruskall, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison-Wesley, Reading, MA, 1983].