wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Such a spanner could withstand a catastrophe: failureof even{\em    90\\%DIF < of the network.
Revised:  Such a spanner could withstand a catastrophe: failureof even{\em for the Euclidean space. A highly desirable feature of a reliable spanner is its ability to withstand a massive failure: the network remains functioning even if 90\\%DIF < of the network.
Edit intent: meaning-changed
Original:  We find that dissemination was ( originally ) limited to a few sub-communities and that, while heavy-handed content moderation decisions have reduced the overall issue, the "gospel" of Q persists on Web communities .
Revised:  We find that dissemination was ( initially ) limited to a few sub-communities and that, while heavy-handed content moderation decisions have reduced the overall issue, the "gospel" of Q persists on Web communities .
Edit intent: fluency
Original:  We find that dissemination was ( originally ) limited to a few sub-communities and that, while heavy-handed content moderation decisions have reduced the overall issue, the "gospel" of Q persists on Web communities .
Revised:  We find that dissemination was ( originally ) limited to a few sub-communities and that, while heavy-handed moderation decisions have reduced the overall issue, the "gospel" of Q persists on Web communities .
Edit intent: clarity
Original:  We find that dissemination was ( originally ) limited to a few sub-communities and that, while heavy-handed content moderation decisions have reduced the overall issue, the "gospel" of Q persists on Web communities .
Revised:  We find that dissemination was ( originally ) limited to a few sub-communities and that, while heavy-handed content moderation decisions have reduced the overall issue, the "gospel" of Q persists on the Web .
Edit intent: clarity
Original: A k-apex graph is a graph with a subset of k vertices, called apices, whose removal makes the graph planar. We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised: We give an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: clarity
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^3 n \ )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: clarity
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^2 n \log^3 npolylog )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: meaning-changed
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^2 n \log^3 n(nC) )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: meaning-changed
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^2 n \log^3 n )-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks . This improves by a factor of k on the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: meaning-changed
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k ^2 over the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: clarity
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ Wang, SODA 2019 Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: meaning-changed
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] .
Revised:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ . The speedup is obtained by two independent ideas. First we replace an iterative procedure of Wang that uses k invocations of a maximum flow algorithm in a planar graph with k apices Borradaile et al., FOCS 2012, SICOMP 2017] .
Edit intent: meaning-changed
Original:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [   Borradaile et al., FOCS 2012, SICOMP 2017] . Our improvement is achieved by introducing a new variant of the push-relabel algorithm for computing maximum flows.
Revised:  We present an O(k ^2 n \log^3 n )-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinksT, computes a maximum flow from S to T in G . This improves by a factor of k on the fastest algorithm previously known for this problem [ Borradaile et al., FOCS 2012, SICOMP 2017] , by an alternative procedure that only makes one invocation of the algorithm of Borradaile et al. Second, we introduce a new variant of the push-relabel algorithm for computing maximum flows.
Edit intent: meaning-changed
Original:  Our improvement is achieved by introducing a new variant of the push-relabel algorithm for computing maximum flows. We use our improved algorithm for maximum flow in  k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Revised:  Our improvement is achieved by introducing a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original:  We use our improved algorithm for maximum flow in  k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Revised:  We use our improved algorithm for maximum flow in the k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Edit intent: fluency
Original:  We use our improved algorithm for maximum flow in  k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Revised:  We use our improved algorithm for maximum flow in k-apex graphs \textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Edit intent: clarity
Original:  We use our improved algorithm for maximum flow in  k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Revised:  We use our improved algorithm for maximum flow in k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{ (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original:  We use our improved algorithm for maximum flow in  k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog (nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks. This improves by a factor of k^2 over the fastest algorithm previously known for this problem%DIFDELCMD < [%%% Wang, SODA 2019 .
Revised:  We use our improved algorithm for maximum flow in k-apex graphs , together with additional insights, to obtain an O(k^3 n \\textrm{polylog %DIFDELCMD < [%%% Wang, SODA 2019 .
Edit intent: coherence
Original:  This improves by a factor of k^2 over the fastest algorithm previously known for this problem%DIFDELCMD < [%%% Wang, SODA 2019 .
Revised:  This improves by a factor of k^2 over the fastest algorithm previously known for this problem%DIFDELCMD < [%%% that arise in Wang's procedure, faster than the algorithm of Borradaile et al .
Edit intent: meaning-changed
Original: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em  capacities bounded by C, and k sources and sinks.
Revised: We give an O(k^3 n polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em  capacities bounded by C, and k sources and sinks.
Revised: We give an O(k^3 n \ ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em  capacities bounded by C, and k sources and sinks.
Revised: We give an O(k^3 n \polylog \log n \min(k,\log^2 n) \log^2( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em  capacities bounded by C, and k sources and sinks.
Revised: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc {\em capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em  capacities bounded by C, and k sources and sinks.
Revised: We give an O(k^3 n \polylog ( nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex {\em and vertex capacities bounded by C, and k sources and sinks.
Edit intent: meaning-changed
Original:  First we replace an iterative procedure of Wang that uses k invocations of a maximum flow algorithm in a planar graph with k apices [Borradaile et al., FOCS 2012, SICOMP 2017], by an alternative procedure that only makes one invocation of the algorithm of Borradaile et al.
Revised:  First we replace an iterative procedure of Wang that uses O(k) invocations of an O(k^3 n \log^3 n)-time algorithm for maximum flow algorithm in a planar graph with k apices [Borradaile et al., FOCS 2012, SICOMP 2017], by an alternative procedure that only makes one invocation of the algorithm of Borradaile et al.
Edit intent: meaning-changed
Original:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in  Wang's procedure , faster than the algorithm of Borradaile et al   .
Revised:  Second, we show two alternatives for computing flows in the k-apex graphs that arise in Wang's procedure , faster than the algorithm of Borradaile et al .
Edit intent: clarity
Original:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in  Wang's procedure , faster than the algorithm of Borradaile et al   .
Revised:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in our modification of Wang's procedure , faster than the algorithm of Borradaile et al .
Edit intent: meaning-changed
Original:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in  Wang's procedure , faster than the algorithm of Borradaile et al   .
Revised:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in Wang's procedure faster than the algorithm of Borradaile et al .
Edit intent: fluency
Original:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in  Wang's procedure , faster than the algorithm of Borradaile et al   .
Revised:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in Wang's procedure , faster than the algorithm of Borradaile et al . In doing so, we introduce and analyze a sequential implementation of the parallel highest-distance push-relabel algorithm of Goldberg and Tarjan~ .
Edit intent: meaning-changed
Original:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in  Wang's procedure , faster than the algorithm of Borradaile et al   .
Revised:  Second, we introduce a new variant of the push-relabel algorithm of Goldberg and Tarjan and use it to find a maximum flow in the k-apex graphs that arise in Wang's procedure , faster than the algorithm of Borradaile et al JACM 1988 .
Edit intent: meaning-changed
Original: We study full acyclic join queries with general join predicates that involve conjunctions and disjunctions of inequalities  , focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function.
Revised: We study theta-joins in general and join predicates with conjunctions and disjunctions of inequalities , focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function.
Edit intent: meaning-changed
Original: We study full acyclic join queries with general join predicates that involve conjunctions and disjunctions of inequalities  , focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function.
Revised: We study full acyclic join queries with general join predicates that involve conjunctions and disjunctions of inequalities in particular , focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function.
Edit intent: meaning-changed
Original:  Our approach offers strong time and space complexity guarantees in the standard RAM model of computation, getting surprisingly close to those of equi-joins. With n denoting the number of tuples in the database, we guarantee  that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k  k) time and \mathcal{O n + k) space .
Revised:  Our approach offers strong time and space complexity properties: with n denoting the number of tuples in the database, we guarantee that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k k) time and \mathcal{O n + k) space .
Edit intent: clarity
Original:  With n denoting the number of tuples in the database, we guarantee  that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k  k) time and \mathcal{O n + k) space .
Revised:  With n denoting the number of tuples in the database, we guarantee for acyclic full join queries with inequality conditions that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k k) time and \mathcal{O n + k) space .
Edit intent: meaning-changed
Original:  With n denoting the number of tuples in the database, we guarantee  that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k  k) time and \mathcal{O n + k) space .
Revised:  With n denoting the number of tuples in the database, we guarantee that for every value of k, the k top-ranked answers are returned in O (n polylog n + k k) time and \mathcal{O n + k) space .
Edit intent: fluency
Original:  With n denoting the number of tuples in the database, we guarantee  that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k  k) time and \mathcal{O n + k) space .
Revised:  With n denoting the number of tuples in the database, we guarantee that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k \log k) time and \mathcal{O n + k) space .
Edit intent: meaning-changed
Original:  With n denoting the number of tuples in the database, we guarantee  that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k  k) time and \mathcal{O n + k) space .
Revised:  With n denoting the number of tuples in the database, we guarantee that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k k) time n + k) space .
Edit intent: clarity
Original:  With n denoting the number of tuples in the database, we guarantee  that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k  k) time and \mathcal{O n + k) space .
Revised:  With n denoting the number of tuples in the database, we guarantee that for every value of k, the k top-ranked answers are returned in \mathcal{O (n polylog n + k k) time and \mathcal{O .
Edit intent: clarity
Original:  This is within a polylogarithmic factor of the best-known guarantee for equi-joins and even  \mathcal{O}(n+k), the time it takes to look at the input and output k answers .
Revised:  This is within a polylogarithmic factor of the best known complexity for equi-joins and even \mathcal{O}(n+k), the time it takes to look at the input and output k answers .
Edit intent: meaning-changed
Original:  This is within a polylogarithmic factor of the best-known guarantee for equi-joins and even  \mathcal{O}(n+k), the time it takes to look at the input and output k answers .
Revised:  This is within a polylogarithmic factor of the best-known guarantee for equi-joins and even of \mathcal{O}(n+k), the time it takes to look at the input and output k answers .
Edit intent: clarity
Original:  This is within a polylogarithmic factor of the best-known guarantee for equi-joins and even  \mathcal{O}(n+k), the time it takes to look at the input and output k answers .
Revised:  This is within a polylogarithmic factor of the best-known guarantee for equi-joins and even \mathcal{O}(n+k), the time it takes to look at the input and return k answers in any order. Our guarantees extend to join queries with selections and many types of projections, such as the so-called free-connex queries. Remarkably, they hold even when the entire output is of size n^\ell for a join of \ell relations.
Edit intent: meaning-changed
Original:  The key ingredient is an \mathcal{O}(n \operatorname{polylog} n)-size factorized representation of the query output, which is constructed on-the-fly for a given query and database.
Revised:  The key ingredient is a novel \mathcal{O}(n \operatorname{polylog} n)-size factorized representation of the query output, which is constructed on-the-fly for a given query and database.
Edit intent: clarity
Original:  As a side benefit, our techniques are also applicable to unranked enumeration (where answers can be returned in any order) for joins with inequalities, returning k answers in \mathcal{O(n }%DIFDELCMD < \operatorname{polylog} %%% n + k).
Revised:  (n }%DIFDELCMD < \operatorname{polylog} %%% n + k).
Edit intent: meaning-changed