wanyu/IteraTeR_v2 huggingface dataset:
Original:  Using elementary combinatorial arguments and symmetry properties, Babai and Gorodezky (SODA 2007,[2]) demonstrated a bound of O(n^30) on the transience class of an n?xn grid.
Revised:  Using elementary combinatorial arguments and symmetry properties, Babai and Gorodezky (SODA 2007,[2]) demonstrated a bound of O(n^30) on the transience class of an nxn grid.
Edit intent: fluency
Original: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs  - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and the other two on L_{2}.
Revised: Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a natural graph class that generalizes both interval and permutation graphs, namely simple-triangle graphs - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and the other two on L_{2}.
Edit intent: coherence
Original: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs  - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and the other two on L_{2}.
Revised: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs . Simple-triangle graphs - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and the other two on L_{2}.
Edit intent: fluency
Original: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs  - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and the other two on L_{2}.
Revised: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs - also known as PI graphs (for Point-Interval) - are the intersection graphs of triangles that are defined by a point on a line L_{1} and the other two on L_{2}.
Edit intent: clarity
Original: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs  - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and the other two on L_{2}.
Revised: Permutation and trapezoid graphs are the intersection graphs of line segments and of trapezoids between two parallel lines L_{1 simple-triangle graphs - also known as PI graphs (for Point-Interval) - where the intersecting objects are triangles with one endpoint on L_{1} and an interval on a parallel line L_{2}.
Edit intent: clarity
Original:  However not much is known for the recognition of partial orders P that are the intersection of orders from different classes P_{1 the recognition of linear-interval orders, i.e. of  orders P=P_{1}\cap P_{2}, where P_{1} is a linear order and P_{2} is an interval order.
Revised:  However not much is known for the recognition of partial orders P that are the intersection of orders from different classes P_{1 the recognition of linear-interval orders, i.e. of partial orders P=P_{1}\cap P_{2}, where P_{1} is a linear order and P_{2} is an interval order.
Edit intent: fluency
Original:  For a graph G with n vertices, where its complement has m edges, our algorithm computes in O(n^{2m) time a simple-triangle representation of G, or it announces that such one does not exist.
Revised:  For a graph G with n vertices, where its complement m) time a simple-triangle representation of G, or it announces that such one does not exist.
Edit intent: clarity
Original:  Using the theory of graph limits, we show how to recognize graph sequences produced by random graphs with a linear embedding (a natural embedding into %DIFDELCMD < \Rrr%%%  ).
Revised:  Using the theory of graph limits, we show how to recognize graph sequences produced by random graph processes with a linear embedding (a natural embedding into %DIFDELCMD < \Rrr%%% ).
Edit intent: clarity
Original:  We define an operator \Gamma which applies to graph limits, which assumes a value zero precisely for graph limits of random graphs with a linear embedding.
Revised:  We define an operator \Gamma which applies to graph limits, which assumes the value zero precisely for graph limits of random graphs with a linear embedding.
Edit intent: fluency
Original:  We define an operator \Gamma which applies to graph limits, which assumes a value zero precisely for graph limits of random graphs with a linear embedding.
Revised:  We define an operator \Gamma which applies to graph limits, which assumes a value zero precisely for graph limits with a linear embedding.
Edit intent: clarity
Original:  Moreover  we introduce a corresponding graph parameter \Gamma^* and show that, for graph sequences which converge to a graph limit under the cut-norm, the \Gamma^*-values converge to the \Gamma-value of the limit .
Revised:  Moreover , we introduce a corresponding graph parameter \Gamma^* and show that, for graph sequences which converge to a graph limit under the cut-norm, the \Gamma^*-values converge to the \Gamma-value of the limit .
Edit intent: fluency
Original:  We ] define an operator \Gamma which applies to graph limits,  which assumes the value zero precisely for graph limits with a linear embedding.
Revised:  We ] define an operator \Gamma which applies to graph limits, and which assumes the value zero precisely for graph limits with a linear embedding.
Edit intent: coherence
Original:  We ] define an operator \Gamma which applies to graph limits,  which assumes the value zero precisely for graph limits with a linear embedding.
Revised:  We ] define an operator \Gamma which applies to graph limits, which assumes the value zero precisely for graph limits that have a linear embedding.
Edit intent: fluency
Original: Probabilistic range query (PRQ) over uncertain moving objects , recently, is attracting more and more attentions  due to the fact it can help people extract their interested moving objects with quantitative probability.
Revised: Recently, probabilistic range query (PRQ) over uncertain moving objects , recently, is attracting more and more attentions due to the fact it can help people extract their interested moving objects with quantitative probability.
Edit intent: coherence
Original: Probabilistic range query (PRQ) over uncertain moving objects , recently, is attracting more and more attentions  due to the fact it can help people extract their interested moving objects with quantitative probability.
Revised: Probabilistic range query (PRQ) over uncertain moving objects is attracting more and more attentions due to the fact it can help people extract their interested moving objects with quantitative probability.
Edit intent: coherence
Original: Probabilistic range query (PRQ) over uncertain moving objects , recently, is attracting more and more attentions  due to the fact it can help people extract their interested moving objects with quantitative probability.
Revised: Probabilistic range query (PRQ) over uncertain moving objects , recently, is attracting more and more attentions , due to the fact it can help people extract their interested moving objects with quantitative probability.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networksq where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networksr where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networksoad where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networksn where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networks where the roads are represented as a series of line segments , we call this kind of query as " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query asq " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query asuery processing on " coarse-grained " query.
Edit intent: clarity
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query asr " coarse-grained " query.
Edit intent: fluency
Original:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query as " coarse-grained " query.
Revised:  Regarding to the former, it is feasible for query processing on road networks where the roads are took as a series of line segments , we call this kind of query asegion (called " coarse-grained " query.
Edit intent: clarity
Original:  For the later, it is suitable for query processing on region , but it is impractical in real applications since various obstacles may limit the movement of moving objects.
Revised:  For the later, it is suitable for "qR" , but it is impractical in real applications since various obstacles may limit the movement of moving objects.
Edit intent: clarity
Original:  In this paper, we introduce the concept of restricted areas, and we are interesting in " fine-grained " query . Specifically, we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Revised:  In this paper, we introduce the concept of restricted areas, and we are interested in " fine-grained " query . Specifically, we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Edit intent: fluency
Original:  In this paper, we introduce the concept of restricted areas, and we are interesting in " fine-grained " query . Specifically, we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Revised:  In this paper, we introduce the concept of restricted areas, and we are interesting in " fine-grained " . Specifically, we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Edit intent: coherence
Original:  Obviously, achieving these goals is significant, since it is closer to the real applications, and contributes to returning more authentic answers.
Revised:  To achieve these goals is significant, since it is closer to the real applications, and contributes to returning more authentic answers.
Edit intent: coherence
Original: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted more and more attentions, due to the fact it can help people extract their interested moving objects with quantitative probability.
Revised: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted more and more attentions, due to the fact it can help people return their interested moving objects with quantitative probability.
Edit intent: clarity
Original:  Previous works usually assumed objects moving on a well defined route, or assumed objects moving freely in 2D space.
Revised:  Previous works usually assumed objects moving freely in 2D space.
Edit intent: coherence
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  q uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Edit intent: coherence
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  The first assumption is appropriate for uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Edit intent: fluency
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  The first assumption is appropriate forq r oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Edit intent: clarity
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  The first assumption is appropriate forq uery processing on oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Edit intent: fluency
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  The first assumption is appropriate forq uery processing onr n etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Edit intent: fluency
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  The first assumption is appropriate forq uery processing onr oad etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Edit intent: fluency
Original:  The first assumption is appropriate forq uery processing onr oadn etworks (called "qRN" for convenience) where the roads are represented as a series of line segments.
Revised:  The first assumption is appropriate forq uery processing onr oadn 
Edit intent: clarity
Original:  This assumption, however, can not work forq uery processing onr egion (called "qR").
Revised:  This assumption, however, q uery processing onr egion (called "qR").
Edit intent: clarity
Original:  This assumption, however, can not work forq uery processing onr egion (called "qR").
Revised:  This assumption, however, can not work for uery processing onr egion (called "qR").
Edit intent: fluency
Original:  This assumption, however, can not work forq uery processing onr egion (called "qR").
Revised:  This assumption, however, can not work forq r egion (called "qR").
Edit intent: clarity
Original:  This assumption, however, can not work forq uery processing onr egion (called "qR").
Revised:  This assumption, however, can not work forq uery processing on egion (called "qR").
Edit intent: fluency
Original:  In thispaper , we introduce the concept of restricted areas, and we are interested in "qR" . Specifically,  we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Revised:  In thispaper , we introduce the concept of restricted area . Specifically, we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Edit intent: coherence
Original:  In thispaper , we introduce the concept of restricted areas, and we are interested in "qR" . Specifically,  we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Revised:  In thispaper , we introduce the concept of restricted areas, and we are interested in "qR" . Specifically, in this paper we consider the problem of PRQ over uncertain moving objects in constrained 2D space.
Edit intent: coherence
Original: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted more and more attentions, due to the fact it can help people return their interested moving objects together with quantitative probabilities.
Revised: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted an ever increasing attention, as it can help people return their interested moving objects together with quantitative probabilities.
Edit intent: clarity
Original: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted more and more attentions, due to the fact it can help people return their interested moving objects together with quantitative probabilities.
Revised: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted more and more attentions, due to the fact it can help people return the interested moving objects together with quantitative probabilities.
Edit intent: clarity
Original:  Most of existing works usually assumed objects moving freely in 2D space.
Revised:  Most of existing works usually assume objects are moving freely in 2D space.
Edit intent: clarity
Original:  This assumption, however, is impractical in real applications since various obstacles may limit the movement of  moving objects.
Revised:  This assumption, however, is impractical in real applications since various obstacles may limit the movement of the moving objects.
Edit intent: fluency
Original:  Inspired by this, we introduce the concept of restricted area.
Edit intent: coherence
Original:  We analyse its unique properties and show that it is infeasible to tackle this problem in a direct way.
Revised:  We analyse its unique properties and show that it is infeasible to solve this problem in a direct way.
Edit intent: clarity
Original:  We demonstrated the effectiveness and efficiency of our proposed approaches by extensive experiments under various experimental settings.
Revised:  We demonstrate the effectiveness and efficiency of our proposed approaches by extensive experiments under various experimental settings.
Edit intent: fluency
Original:  We demonstrated the effectiveness and efficiency of our proposed approaches by extensive experiments under various experimental settings.
Revised:  We demonstrated the effectiveness and efficiency of our proposed approaches through extensive experiments under various experimental settings.
Edit intent: fluency
Original: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted an ever increasing attention, as it can help people return the interested moving objects together with quantitative probabilities .
Revised: Probabilistic range query (PRQ) over uncertain moving objects has attracted an ever increasing attention, as it can help people return the interested moving objects together with quantitative probabilities .
Edit intent: coherence
Original: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted an ever increasing attention, as it can help people return the interested moving objects together with quantitative probabilities .
Revised: Recently, probabilistic range query (PRQ) over uncertain moving objects has attracted much attentions in recent years .
Edit intent: clarity
Original:  Most of existing works usually assume objects are moving freely in  2D space.
Revised:  Most of existing works usually assume objects are moving freely in two-dimensional ( 2D space.
Edit intent: clarity
Original:  Specifically, in this paper we consider the problem of PRQ over uncertain moving objects {in  constrained 2D space} .
Revised:  Specifically, in this paper we consider the problem of PRQ over uncertain moving objects {in a constrained 2D space} .
Edit intent: fluency
Original:  In order to tackle it, we first propose an elementary solution, then develop a suit of optimized strategies for further improving the efficiency \romannumeral \romannumeral   .
Revised:  In order to tackle it, we first propose an elementary solution, then develop a suit of optimized strategies for further improving the efficiency \romannumeral \romannumeral span .
Edit intent: clarity
Original:  In contrast, this paper studies the PRQ over objects moving in a constrained 2D space%DIFDELCMD < } %%% where objects are forbidden to be located in some specific areas.
Revised:  In contrast, this paper studies the PRQ over objects moving %DIFDELCMD < } %%% where objects are forbidden to be located in some specific areas.
Edit intent: clarity
Original:  The key idea of our solution is to use a strategy called pre-approximation that can reduce the initial problem to a highly simplified version, implying that it makes the rest of steps easy to tackle.
Revised:  The key idea of our method is to use a strategy called pre-approximation that can reduce the initial problem to a highly simplified version, implying that it makes the rest of steps easy to tackle.
Edit intent: clarity
Original:  We demonstrate the effectiveness and efficiency of our proposed approaches through extensive experiments under various experimental settings , and highlight an extra finding, i.e., the precomputation based approach suffers a non-trivial preprocessing time, which offers an important indication sign for the future research .
Revised:  We demonstrate the effectiveness and efficiency of our proposed approaches through extensive experiments under various experimental settings .
Edit intent: coherence
Original:  A near-linear time algorithm is given to find in a graph with an Eulerian orientation a second perfect matching of opposite sign , in contrastto the complementary pivoting algorithm which may be exponential.
Revised:  A near-linear time algorithm is given for the following problem: given a graph with an Eulerian orientation a second perfect matching of opposite sign , in contrastto the complementary pivoting algorithm which may be exponential.
Edit intent: clarity