Fast Algorithms for Computing Tree LCS

Mozes, Shay; Tsur, Dekel; Weimann, Oren; Ziv-Ukelson, Michal

doi:10.1007/978-3-540-69068-9_22

Cited by 7 publications

(11 citation statements)

References 24 publications

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“…Our set of problems are very different from the traditional LCS problems for higher dimensional structures [15,1]. All of them are duals of the edit distance problem and our problems aren't.…”

Section: Taxonomy Of Problemsmentioning

confidence: 99%

“…This is solved by a dynamic programming algorithm. [15] tries to generalize the problem to find the LCS of two trees. Here the dual of the LCS is a node deletion based edit distance metric.…”

Section: Related Workmentioning

confidence: 99%

“…There is one similarity in the definition of LCS for higher dimensional structures in all the previous works [1,15]. Their variant of LCS is the dual of the minimum edit distance problem, which can be stated as follows.…”

Section: Introductionmentioning

confidence: 97%

“…RNAs have secondary and tertiary structures that require common regions between two directed acyclic graphs [3,13]. Sadly other than the basic LCS problem and variants of it like TreeLCS [15], other problems have either not deserved enough attention or have been proven to be NP-Complete. For example, a recent paper [1] generalizes LCS to matrices and forests, and proves both the problems to be NP Complete.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical Framework for Eliminating Redundancy in Workflows

Saha

Samanta

Sarangi

2009

2009 IEEE International Conference on Services Computing

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In this paper we look at combining and compressing a set of workflows, such that computation can be minimized. In this context, we look at two novel theoretical problems with applications in workflow systems and services research, which are duals of each other. The first problem looks at merging the maximum number of vertices in two DAGs (directed acyclic graphs) without creating a cycle. We prove that the dual of this problem is the problem of maximizing the length of the LCS (longest common subsequence) between all pairs of topological orderings of the two DAGs. This formulation generalizes to a new definition of LCS between complex structures like workflows or XML documents, which we call M-LCS. Subsequently, we present a taxonomy of the different kinds of problems in this set, and find the M-LCS solution for a tree and a chain with a dynamic programming algorithm. Along with this theoretical formulation, we implement the algorithms in C++ and run it on representative workflows. We evaluate the performance of the M-LCS algorithm on a set of random workflows and observe that it is substantially better than traditional AI based approaches.

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Section: Taxonomy Of Problemsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Theoretical Framework for Eliminating Redundancy in Workflows

Saha

Samanta

Sarangi

2009

2009 IEEE International Conference on Services Computing

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“…In the second part of this paper, we perform a similar complexity analysis on a weighted variant of LCS. This follows the majority of recent work on LCS, which focused on transferring the early successes and techniques to more complicated problems, such as longest common increasing subsequence [39,33,52,17], tree LCS [41], and many more generalizations and variants of LCS, see, e.g., [32,15,48,28,3,34,30,21,45,25]. For brevity, here we ignore the equally vast literature on the closely related edit distance.…”

Section: Further Related Workmentioning

confidence: 99%

Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS

Bringmann

Chaudhury

2018

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We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size |Σ|. For the problem of deciding whether the LCS of strings x, y has length at least L, we obtain a sketch size and streaming space usage of O(L |Σ|−1 log L). We also prove matching unconditional lower bounds.As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an O(min{nm, n + m |Σ| })-time algorithm for this problem, on strings x, y of length n, m, with n ≥ m. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis.

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Theoretical Analysis of Git Bisect

Courtiel,

Dorbec,

Lecoq

2023

Algorithmica

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In this paper, we consider the problem of finding a regression in a version control system (VCS), such as git. The set of versions is modelled by a Directed Acyclic Graph (DAG) where vertices represent versions of the software, and arcs are the changes between different versions. We assume that somewhere in the DAG, a bug was introduced, which persists in all of its subsequent versions. It is possible to query a vertex to check whether the corresponding version carries the bug. Given a DAG and a bugged vertex, the Regression Search Problem consists in finding the first vertex containing the bug in a minimum number of queries in the worst-case scenario. This problem is known to be NP-complete. We study the algorithm used in git to address this problem, known as git bisect. We prove that in a general setting, git bisect can use an exponentially larger number of queries than an optimal algorithm. We also consider the restriction where all vertices have indegree at most 2 (i.e. where merges are made between at most two branches at a time in the VCS), and prove that in this case, git bisect is a 1 log 2 (3/2) -approximation algorithm, and that this bound is tight. We also provide a better approximation algorithm for this case. Finally, we give an alternative proof of the NP-completeness of the Regression Search Problem, via a variation with bounded indegree.

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Fast Algorithms for Computing Tree LCS

Cited by 7 publications

References 24 publications

Theoretical Framework for Eliminating Redundancy in Workflows

Theoretical Framework for Eliminating Redundancy in Workflows

Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS

Theoretical Analysis of Git Bisect

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