Predicting Gene Structures from Multiple RT-PCR Tests

Kováč, Jakub; Vinař, Tomáš; Brejová, Broňa

doi:10.1007/978-3-642-04241-6_16

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…The PAFP problem on directed acyclic graphs also arose in a completely different application in bioinformaticsgene finding using RT-PCR tests [5]. In this application, we have a so called splicing graph where vertices represent non-overlapping segments of the DNA sequence, length of a vertex is the number of nucleotides in this segment, and edge (u, v) indicates that segment v immediately follows segment u in some gene transcript.…”

Section: Motivationmentioning

confidence: 99%

“…• find an s-t path passing the minimum number of forbidden pairs or • given a graph where all edges have scores and there are bonuses or penalties for some (well-parenthesized) pairs of vertices, find an s-t path with maximum score (a problem motivated by an application in gene finding [5]).…”

Section: Well-parenthesized Forbidden Pairsmentioning

confidence: 99%

“…The research of Jakub Kováč is supported by APVV grant SK-CN-0007-09, Marie Curie Fellowship IRG-231025 to Dr. Broňa Brejová, Comenius University grant UK/121/2011, and by National Scholarship Programme (SAIA), Slovak Republic. Preliminary version of this work appeared in Kováč et al [5].…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Thus, the PAFP problem is at the core of gene finding with RT-PCR tests and the latter problem inherits all NP-hardness results for the PAFP problem. On the positive side, we have shown in our previous work [5] that some polynomial solutions for special cases of the PAFP problem can be extended to pseudo-polynomial algorithms for the gene finding problem.…”

Section: Motivationmentioning

confidence: 99%

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Complexity of the path avoiding forbidden pairs problem revisited

Kováč¹

2013

Discrete Applied Mathematics

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Let G = (V, E) be a directed acyclic graph with two distinguished vertices s, t, and let F be a set of forbidden pairs of vertices. We say that a path in G is safe, if it contains at most one vertex from each pair {u, v} ∈ F. Given G and F, the path avoiding forbidden pairs (PAFP) problem is to find a safe s-t path in G.We systematically study the complexity of different special cases of the PAFP problem defined by the mutual positions of fobidden pairs. Fix one topological ordering ≺ of vertices; we say that pairs {u, v} and {x, y} are disjoint,The PAFP problem is known to be NP-hard in general or if no two pairs are disjoint; we prove that it remains NP-hard even when no two forbidden pairs are nested. On the other hand, if no two pairs are halving, the problem is known to be solvable in cubic time. We simplify and improve this result by showing an O(M(n)) time algorithm, where M(n) is the time to multiply two n × n boolean matrices.

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Section: Motivationmentioning

confidence: 99%

Section: Well-parenthesized Forbidden Pairsmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

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Complexity of the path avoiding forbidden pairs problem revisited

Kováč¹

2013

Discrete Applied Mathematics

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“…In the latter problem one is given a set of arc pairs A and has to identify whether some s-t-path avoids all pairs in A (meaning SFP asks for a set that makes the corresponding PAFP instance unsolvable). Originating from the field of automated software testing [27], PAFP also has applications in aircraft routing [7] and biology, for example in peptide sequencing [8] or predicting gene structures [26]. The PAFP is NP-complete [17] and various restrictions on the set of forbidden pairs have been considered.…”

Section: Introductionmentioning

confidence: 99%

Almost Disjoint Paths and Separating by Forbidden Pairs

Bachtler¹,

Bergner²,

Krumke³

2022

Preprint

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By Menger's theorem the maximum number of arc-disjoint paths from a vertex s to a vertex t in a directed graph equals the minumum number of arcs needed to disconnect s and t, i.e., the minimum size of an s-t-cut. The max-flow problem in a network with unit capacities is equivalent to the arc-disjoint paths problem. Moreover the max-flow and min-cut problems form a strongly dual pair. We relax the disjointedness requirement on the paths, allowing them to be almost disjoint, meaning they may share up to one arc. The resulting almost disjoint paths problem (ADP) asks for k s-t-paths such that any two of them are almost disjoint. The separating by forbidden pairs problem (SFP) is the corresponding dual problem and calls for a set of k arc pairs such that every s-t-path contains both arcs of at least one such pair. In this paper, we explore these two problems, showing that they have an unbounded duality gap in general and analyzing their complexity. We prove that ADP is NP-complete when k is part of the input and that SFP is Σ2P-complete, even for acyclic graphs. Furthermore, we efficiently solve ADP when k ≤ 2 is fixed and present a polynomial time algorithm based on dynamic programming for ADP when k is constant and the considered graphs are acyclic.

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