wanyu/IteraTeR_full_sent huggingface dataset:
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G if G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any induced cycle on more than~t vertices. We prove the following statement: for every pair of integers d and t and a CMSO_2 statement~\phi, there exists an algorithm that, given an n-vertex C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ >t }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph G with weights on vertices, finds in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: clarity
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^4 n) , and therefore for fixed k is a quasi-polynomial time algorithm.
Edit intent: meaning-changed
Original: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G  does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) , and therefore for fixed k is a quasi-polynomial time algorithm. C_{\geq 4-free graphs (also known as chordal graphs) have a well known polynomial time algorithm.
Revised: We give an algorithm that takes as input a graph G with weights on the vertices and outputs a maximum weight independent set of G . If G does not contain any cycle on k or more vertices as an induced subgraph (G is a C _{ \geq k }-free graph ), the algorithm runs in time n^{O( k^3 \log ^5 n) -free graphs (also known as chordal graphs) have a well known polynomial time algorithm.
Edit intent: coherence
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } a maximum-weight vertex subset S such that G [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Edit intent: meaning-changed
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ S ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Edit intent: meaning-changed
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ Chudnovsky et al., Arxiv'19 ] has degeneracy at most d and satisfies \phi. The running time can be improved to n^{O(\log^2 n) -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Edit intent: meaning-changed
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free , that is, G does not contain an induced path on t vertices. This expands the recent results of the authors [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Edit intent: meaning-changed
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ to appear at FOCS 2020 and SOSA 2021 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Edit intent: meaning-changed
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Edit intent: clarity
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme %DIFDELCMD < ] %%% was known.
Edit intent: coherence
Original:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 }  [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% was known. Our work is the first to exhibit conclusive evidence that Independent Set on C_{\geq k{\sc{Maximum Weight Independent Set}}  -free graphs isnot NP-complete for any integer k.
Revised:  A subexponetial time algorithm for C_{\geq 5}-free graphs (also known as long-hole-free graphs) was found in 2019 } [ Chudnovsky et al., Arxiv'19 ] followed by a polynomial time algorithm for C_{\geq 5 -free graphs in 2020 [ Abrishami et al. , Arxiv'20 ] . For k > 5 only a quasi-polynomial time approximation scheme Chudnovsky et al., SODA'20%DIFDELCMD < ] %%% on the{\sc{Maximum Weight Independent Set}} -free graphs isnot NP-complete for any integer k.
Edit intent: coherence
Original:  Our work is the first to exhibit conclusive evidence that Independent Set on C_{\geq k{\sc{Maximum Weight Independent Set}}  -free graphs isnot NP-complete for any integer k.
Revised:  Our work is the first to exhibit conclusive evidence that Independent Set on C_{\geq k{\sc{Maximum Weight Independent Set}} problem on P_t -free graphs isnot NP-complete for any integer k.
Edit intent: meaning-changed
Original:  Our work is the first to exhibit conclusive evidence that Independent Set on C_{\geq k{\sc{Maximum Weight Independent Set}}  -free graphs isnot NP-complete for any integer k. This also generalizes previous work of ours Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Revised:  Our work is the first to exhibit conclusive evidence that Independent Set on C_{\geq k{\sc{Maximum Weight Independent Set}} -free Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Edit intent: clarity
Original:  This also generalizes previous work of ours Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Revised:  This also generalizes previous work of ours %DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Edit intent: coherence
Original:  This also generalizes previous work of ours Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Revised:  This also generalizes previous work of ours Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% graphs in two directions: by encompassing the more general setting of C_{>t-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Edit intent: meaning-changed
Original:  This also generalizes previous work of ours Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} {\sc{Maximum Weight Induced Planar Graph}} .
Revised:  This also generalizes previous work of ours Gartland and Lokshtanov, FOCS '20%DIFDELCMD < ]%%% , with an additional factor of \log^2(n) in the exponent, where we provided a quasi-polynomial time algorithm for graphs that exclude a path on k vertices as an induced subgraph-free graphs, and by being applicable to a much wider variety of problems, such as }{\sc{Maximum Weight Induced Forest}} or{\sc{Maximum Weight Induced Planar Graph}} .
Edit intent: clarity
Original: Examining field-programmable gate array (FPGA ) bitstream is found to help detect known function blocks, which offers assistance and insight to analyze the circuit's system function. Our goal is to detect one or more than one function block in FPGA design from a complete bitstream by utilizing the latest deep learning techniques, which do not require manually designing features. To this end, in this paper, we propose a  deep learning-based FPGA function block detection method by transforming the bitstream into a three-channel color image .
Revised: In the context of various application scenarios and/or for the sake of strengthening FPGA security, the system functions of an FPGA design need to be analyzed, which can be achieved by systematically partitioning the FPGA's bitstream into manageable functional blocks and detecting their functionalities thereafter. In this paper, we propose a deep learning-based FPGA function block detection method by transforming the bitstream into a three-channel color image .
Edit intent: clarity
Original:  In specific, we first analyze the format of the bitstream to find the mapping relationship between the configuration bits and configurable logic blocks . Next, an image-coded representation of bitstream is proposed suitable for deep learning processing.
Revised:  In specific, we first analyze the format of the bitstream to obtain the mapping relationship between the configuration bits and configurable logic blocks . Next, an image-coded representation of bitstream is proposed suitable for deep learning processing.
Edit intent: clarity
Original:  In specific, we first analyze the format of the bitstream to find the mapping relationship between the configuration bits and configurable logic blocks . Next, an image-coded representation of bitstream is proposed suitable for deep learning processing. This bitstream-to-image transformation takes into account of the adjacency nature of the programmable logic as well as high degree of redundancy of configuration information.
Revised:  In specific, we first analyze the format of the bitstream to find the mapping relationship between the configuration bits and configurable logic blocks because of the discontinuity of the configuration bits in the bitstream for one element. In order to reap the maturity of object detection based on deep learning techniques, our next step is to convert an FPGA bitstream to an image, following the proposed transformation method that takes account of both the adjacency nature of the programmable logic as well as high degree of redundancy of configuration information.
Edit intent: meaning-changed
Original:  With the color images transformed from bitstreams as the training dataset , a deep learning-based object detection algorithm is applied for generating the function block detection results. The effects of EDA tools, input size of the deep neural network , and the data arrangement of representation on the detection accuracy are explored.
Revised:  With the color images transformed from bitstreams as the training dataset , a deep learning-based object detection algorithm is applied to this transformed image, and the objects thus detected can be reflected back to determine the function blocks of the original FPGA design. The deep neural network , and the data arrangement of representation on the detection accuracy are explored.
Edit intent: meaning-changed
Original:  The effects of EDA tools, input size of the deep neural network , and the data arrangement of representation on the detection accuracy are explored. The Xilinx Zynq-7000 SoCs and Xilinx Zynq UltraScale+ MPSoCs are adopted to verify the proposed method, and the results show that the mean Average Precision (IoU=0.5) for 10 function blocks is as high as 97.72\% for YOLOv3 detector  .
Revised:  The effects of EDA tools, input size of the deep neural network used for function block detection is trained and validated with a specially crafted bitstream/image dataset. Experiments have confirmed high detection accuracy of the proposed function detection method, showing a 98.11\% of mean Average Precision (IoU=0.5) for 10 function blocks is as high as 97.72\% for YOLOv3 detector .
Edit intent: meaning-changed
Original:  The Xilinx Zynq-7000 SoCs and Xilinx Zynq UltraScale+ MPSoCs are adopted to verify the proposed method, and the results show that the mean Average Precision (IoU=0.5) for 10 function blocks is as high as 97.72\% for YOLOv3 detector  .
Revised:  The Xilinx Zynq-7000 SoCs and Xilinx Zynq UltraScale+ MPSoCs are adopted to verify the proposed method, and the results show that the mean Average Precision (IoU=0.5) for 10 function blocks within a YOLOv3 detector .
Edit intent: clarity
Original:  The Xilinx Zynq-7000 SoCs and Xilinx Zynq UltraScale+ MPSoCs are adopted to verify the proposed method, and the results show that the mean Average Precision (IoU=0.5) for 10 function blocks is as high as 97.72\% for YOLOv3 detector  .
Revised:  The Xilinx Zynq-7000 SoCs and Xilinx Zynq UltraScale+ MPSoCs are adopted to verify the proposed method, and the results show that the mean Average Precision (IoU=0.5) for 10 function blocks is as high as 97.72\% for YOLOv3 detector implemented on Xilinx Zynq-7000 SoCs and Zynq UltraScale+ MPSoCs .
Edit intent: clarity
Original:  We formalize the process of defeaturing by understanding its effect on the solution of the Laplace equation defined on the geometrical model of interest  , with Neumann boundary conditions on the features themselves .
Revised:  We formalize the process of defeaturing by understanding its effect on the solution of the Laplace equation defined on the geometrical model of interest containing a single feature , with Neumann boundary conditions on the features themselves .
Edit intent: meaning-changed
Original:  We derive an a posteriori estimator of the energy error between the solutions of the exact and the defeatured geometries in R^n,  that is simple, efficient and reliable up to oscillations.
Revised:  We derive an a posteriori estimator of the energy error between the solutions of the exact and the defeatured geometries in R^n, n\in\{2,3\ that is simple, efficient and reliable up to oscillations.
Edit intent: meaning-changed
Original:  We give a similar result when item size distributions are exponential with arbitrary rates  .
Revised:  We give a similar result when item size distributions are exponential with arbitrary rates . We also study the offline model, where distributions are known in advance but must be packed sequentially. We construct a soft-capacity PTAS for this problem, and show that the complexity of computing the optimal offline cost is \#\mathbf{P .
Edit intent: meaning-changed
Original:  We present polynomial-time kernelizations for Cluster Editing/Deletion , Path Contractions and Feedback Vertex Set that run with O(\mathrm{poly (k) \log n) bits and compute a kernel of size polynomial in k . By first executing the new kernelizations and subsequently the best known polynomial-time kernelizations for the problem under consideration, we obtain the best known kernels in polynomial time with O( \mathrm{poly(k) \log n) bits.
Revised:  We present a full kernel for Path Contraction and Cluster Editing/Deletion , Path Contractions and Feedback Vertex Set that run with O(\mathrm{poly (k) \log n) bits and compute a kernel of size polynomial in k . By first executing the new kernelizations and subsequently the best known polynomial-time kernelizations for the problem under consideration, we obtain the best known kernels in polynomial time with O( \mathrm{poly(k) \log n) bits.
Edit intent: clarity