wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%%  k. This generalizes the %DIFDELCMD < \NP%%% -complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Revised: In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. o Given a permutation group G=< S%DIFDELCMD < }\le %%% S_n and a parameter k, find a permutation \pi \in G such that |{i\in [n]\mid \pi(i)\ne i}| %DIFDELCMD < \ge %%% k. This generalizes the %DIFDELCMD < \NP%%% well-known NP-complete problem of finding a fixed-point free permutation in G CW10,Lub81 (this is the case when k=n).
Edit intent: clarity
Original:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Revised:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Edit intent: coherence
Original:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Revised:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . 2. Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Edit intent: coherence
Original:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Revised:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< %DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Edit intent: clarity
Original:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Revised:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S> . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Edit intent: clarity
Original:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B \subseteq [n] such that the subgroup of G that fixes B pointwise is trivial.
Revised:  In the process, we give a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron C11,CW10 . o Next we consider the problem of computing a base for a permutation group G=< S%DIFDELCMD < }\le %%% S_n . A base for G is a subset B of [n] such that the subgroup of G that fixes B pointwise is trivial.
Edit intent: clarity
Original:  This problem is known to be %DIFDELCMD < \NP%%% -complete B192 .
Revised:  This problem is known to be %DIFDELCMD < \NP%%% B192 .
Edit intent: clarity
Original:  B. Bollob\'{a}s and P. Erd\"{o}s (1976) proposed the following conjecture: If \Delta^{mon} (K_{n}^{c})<\lfloor n{2} \rfloor, then K_{n}^{c} contains a properly colored Hamiltonian cycle.
Revised:  B. Bollob\'{a}s and P. Erd\"{o}s (1976) proposed the following conjecture: if \Delta^{mon} (K_{n}^{c})<\lfloor n{2} \rfloor, then K_{n}^{c} contains a properly colored Hamiltonian cycle.
Edit intent: fluency
Original:  Essentially the same construction produces Theta(log log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those that belong to any class of compact arcwise connected subsets of R ^2 closed under horizontal scaling, vertical scaling, and translation, except for the class of axis-aligned rectangles.
Revised:  Essentially the same construction produces Theta(log log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arcwise connected subsets of R ^2 closed under horizontal scaling, vertical scaling, and translation, except for the class of axis-aligned rectangles.
Edit intent: fluency
Original:  Essentially the same construction produces Theta(log log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those that belong to any class of compact arcwise connected subsets of R ^2 closed under horizontal scaling, vertical scaling, and translation, except for the class of axis-aligned rectangles.
Revised:  Essentially the same construction produces Theta(log log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those that belong to any class of compact arcwise connected subsets of R ^2 closed under horizontal scaling, vertical scaling, and translation, except for axis-aligned rectangles.
Edit intent: clarity
Original:  Namely, we prove that triangle-free intersection graphs of rectangular frames in the plane have chromatic number O( log log n), improving on the previous bound of O( log n).
Revised:  Namely, we prove that triangle-free rectangle overlap graphs have chromatic number O( log log n), improving on the previous bound of O( log n).
Edit intent: clarity
Original:  To this end, we exploit a relationship between off-line coloring of rectangular frame intersection graphs and on-line coloring of interval overlap graphs.
Revised:  To this end, we exploit a relationship between off-line coloring of rectangle overlap graphs and on-line coloring of interval overlap graphs.
Edit intent: clarity
Original: Recently, Pawlik et al. have shown that triangle-free intersection graphs of  line segments in the plane can have arbitrarily large chromatic number . Specifically, they construct triangle-free segment intersection graphs with chromatic number \Theta(\log\log n).
Revised: Recently, Pawlik et al. have shown that triangle-free intersection graphs of line segments in the plane can have chromatic number as large as \Theta(\log\log n).
Edit intent: clarity
Original:  Essentially the same construction produces \Theta(\log\log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arc-connected subsets of R^2 closed under horizontal scaling, vertical scaling, and translation, except for axis-aligned rectangles.
Revised:  Essentially the same construction produces \Theta(\log\log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arc-connected sets in R^2 closed under horizontal scaling, vertical scaling, and translation, except for axis-aligned rectangles.
Edit intent: clarity
Original:  Essentially the same construction produces \Theta(\log\log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arc-connected subsets of R^2 closed under horizontal scaling, vertical scaling, and translation, except for axis-aligned rectangles.
Revised:  Essentially the same construction produces \Theta(\log\log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes---those belonging to any class of compact arc-connected subsets of R^2 closed under horizontal scaling, vertical scaling, and translation, except for axis-parallel rectangles.
Edit intent: clarity
Original:  This class of graphs can be alternatively defined as the class of overlap graphs of axis-aligned rectangles, that is, graphs in which two rectangles are connected by an edge if they intersect but are not nested.
Revised:  This class of graphs can be alternatively described as overlap graphs of axis-aligned rectangles, that is, graphs in which two rectangles are connected by an edge if they intersect but are not nested.
Edit intent: clarity
Original:  Our coloring method decomposes the graph into a bounded number of subgraphs with a tree-like structure that "encodes" strategies of the adversary in the on-line coloring problem , and colors these subgraphs with O(\log\log n) colors using a combination of techniques from on-line algorithms (first-fit) and data structure design (heavy-light decomposition).
Revised:  Our coloring method decomposes the graph into a bounded number of subgraphs with a tree-like structure that "encodes" strategies of the adversary in the on-line coloring problem . Then, these subgraphs are colored with O(\log\log n) colors using a combination of techniques from on-line algorithms (first-fit) and data structure design (heavy-light decomposition).
Edit intent: coherence
Original: Recently, Pawlik et al. have shown that triangle-free intersection graphs of n line segments in the plane can have chromatic number as large as \Theta(\log\log n).
Revised: Recently, it was proved that triangle-free intersection graphs of n line segments in the plane can have chromatic number as large as \Theta(\log\log n).
Edit intent: clarity
Original:  Our contributions can be summarized as follows: enumerate We consider the matroid center problem in which the centers are required to form an independent set of a given matroid.
Revised:  Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid.
Edit intent: coherence
Original:   We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s).
Revised:  2. We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s).
Edit intent: fluency
Original:  We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by 1+\epsilon. enumerate
Revised:  We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by 1+\epsilon. 
Edit intent: clarity
Original:  Additionally, our construction does not suffer from the extra poly-logarithmic factor multiplying the number of observations k as a function of the sparsity s, as present in the presently best known RIP estimates for partial random Fourier matrices and other classes of structured random matrices.
Revised:  Additionally, our construction does not suffer from the extra poly-logarithmic factor multiplying the number of observations k as a function of the sparsity s, as present in the currently best known RIP estimates for partial random Fourier matrices and other classes of structured random matrices.
Edit intent: fluency
Original: A general approach to study and enhance the slope limiter functions on non-uniform grids is presented.
Revised: Most slope limiter functions on non-uniform grids is presented.
Edit intent: clarity
Original:  Several most widely used conventional limiters are enhanced to satisfy these conditions , and their performances are illustrated by various 1D and 2D numerical examples .
Revised:  Several most widely used conventional limiters are enhanced to satisfy these conditions . These properties are confirmed by solving various one-dimensional and two-dimensional benchmark problems using the enhanced limiters on highly non-uniform rectilinear grids .
Edit intent: clarity
Original: Document sets downloaded from the Web of Science can be projected onto global journal maps based on all journals contained in the Journal Citation Reports (JCR) of the Science and Social Science Citation Indices (2011).
Revised: Document sets downloaded from the Web of Science , one can directly generate overlays onto global journal maps based on all journals contained in the Journal Citation Reports (JCR) of the Science and Social Science Citation Indices (2011).
Edit intent: clarity
Original:  The disciplinary diversity of a downloaded set is then measured in terms of this map using Rao-Stirling's "quadratic entropy."
Revised:  The disciplinary diversity of the retrieval is measured in terms of this map using Rao-Stirling's "quadratic entropy."
Edit intent: clarity
Original:  The disciplinary diversity of a downloaded set is then measured in terms of this map using Rao-Stirling's "quadratic entropy."
Revised:  The disciplinary diversity of a downloaded set is then measured in terms of Rao-Stirling's "quadratic entropy."
Edit intent: clarity
Original:  Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity of document sets can be compared among one another and across years, both cited and citing.
Revised:  Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity can be compared among one another and across years, both cited and citing.
Edit intent: clarity
Original:  Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity of document sets can be compared among one another and across years, both cited and citing.
Revised:  Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity of document sets can be compared among document sets and across years, both cited and citing.
Edit intent: clarity
Original:  Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity of document sets can be compared among one another and across years, both cited and citing.
Revised:  Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity of document sets can be compared among one another and across years, cited or citing.
Edit intent: coherence
Original:  The colors used for the overlays are based on Blondel et al.'s (2008) community-finding algorithms operating on the 10,000+ journals included in JCRs.
Revised:  The colors used for the overlays are based on Blondel et al.'s (2008) community-finding algorithms operating on the relations journals included in JCRs.
Edit intent: clarity
Original:  The relations between local and global maps and their different functions in studying the sciences in terms of journal literatures are further discussed: local and global maps will be based on different (analytical) assumptions and can be expected to serve different purposes for the explanation.
Revised:  The relations between local and global maps and their different functions in studying the sciences in terms of journal litteratures are further discussed: local and global maps will be based on different (analytical) assumptions and can be expected to serve different purposes for the explanation.
Edit intent: fluency
Original:  The relations between local and global maps and their different functions in studying the sciences in terms of journal literatures are further discussed: local and global maps will be based on different (analytical) assumptions and can be expected to serve different purposes for the explanation.
Revised:  The relations between local and global maps and their different functions in studying the sciences in terms of journal literatures are further discussed: local and global maps are based on different (analytical) assumptions and can be expected to serve different purposes for the explanation.
Edit intent: fluency
Original:  The relations between local and global maps and their different functions in studying the sciences in terms of journal literatures are further discussed: local and global maps will be based on different (analytical) assumptions and can be expected to serve different purposes for the explanation.
Revised:  The relations between local and global maps and their different functions in studying the sciences in terms of journal literatures are further discussed: local and global maps will be based on different assumptions and can be expected to serve different purposes for the explanation.
Edit intent: clarity
Original: Frequent itemsets mining is a fundamental primitive in data mining , requiring to identify all itemsets that appear in a fraction at least \theta of the transactional dataset .
Revised: Frequent Itemsets (FIs) mining is a fundamental primitive in data mining , requiring to identify all itemsets that appear in a fraction at least \theta of the transactional dataset .
Edit intent: clarity
Original: Frequent itemsets mining is a fundamental primitive in data mining , requiring to identify all itemsets that appear in a fraction at least \theta of the transactional dataset .
Revised: Frequent itemsets mining is a fundamental primitive in data mining that requires to identify all itemsets that appear in a fraction at least \theta of the transactional dataset .
Edit intent: fluency
Original: Frequent itemsets mining is a fundamental primitive in data mining , requiring to identify all itemsets that appear in a fraction at least \theta of the transactional dataset .
Revised: Frequent itemsets mining is a fundamental primitive in data mining , requiring to identify all itemsets appearing in a fraction at least \theta of the transactional dataset .
Edit intent: clarity
Original:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets} , i.e., itemsets A such that theirreal frequency (the probability that A appear in a transaction) is greater or equal to the the minimum threshold \theta .
Revised:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets} , i.e., itemsets real frequency (the probability that A appear in a transaction) is greater or equal to the the minimum threshold \theta .
Edit intent: clarity
Original:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets} , i.e., itemsets A such that theirreal frequency (the probability that A appear in a transaction) is greater or equal to the the minimum threshold \theta .
Revised:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets} , i.e., itemsets A such that their (the probability that A appear in a transaction) is greater or equal to the the minimum threshold \theta .
Edit intent: clarity
Original: In other words, we present a statistical test for RFI's for which we can guarantee that theFamily-Wise Error Rate is within the user-specified limits.
Revised: In other words, we present a statistical test for RFI's for which we can guarantee that the is within the user-specified limits.
Edit intent: clarity
Original:  We use results from statistical learning theory involving the Vapnik-Chervonenkis (VC) dimension of the problem at hand to accomplish this goal .
Revised:  We use results from statistical learning theory involving the (empirical) VC-dimension of the problem at hand to accomplish this goal .
Edit intent: clarity
Original:  We use results from statistical learning theory involving the Vapnik-Chervonenkis (VC) dimension of the problem at hand to accomplish this goal .
Revised:  We use results from statistical learning theory involving the Vapnik-Chervonenkis (VC) dimension of the problem at hand .
Edit intent: clarity
Original:  In our experimental evaluation we show empirically that our test has very high statistical power  .
Revised:  In the experimental evaluation we show empirically that our test has very high statistical power .
Edit intent: fluency
Original:  mining is a fundamental primitive in data mining that requires to identify all itemsets appearing in a fraction at least \theta of a transactional dataset D. Often though,
Revised:  mining is a fundamental primitive in data mining . It requires to identify all itemsets appearing in a fraction at least \theta of a transactional dataset D. Often though,
Edit intent: coherence
Original:  mining is a fundamental primitive in data mining that requires to identify all itemsets appearing in a fraction at least \theta of a transactional dataset D. Often though,
Revised:  mining is a fundamental primitive in data mining that requires to identify all itemsets appearing in at least a fraction \theta of a transactional dataset D. Often though,
Edit intent: fluency
Original:  the ultimate goal of mining D is not an analysis of the dataset per se , but the understanding of the underlying process that generated \mathcal{D . Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution \pi on transactions, and by extracting the FIs in the dataset D one attempts to infer itemsets that are frequently  generated by \pi, which we call the True Frequent Itemsets (TFIs).
Revised:  the ultimate goal of mining D is not an analysis of the dataset per se , but the understanding of the underlying process that generated \mathcal{D . Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution \pi on transactions, and by extracting the FIs in the dataset D one attempts to infer itemsets that are frequently generated by \pi, which we call the True Frequent Itemsets (TFIs).
Edit intent: fluency