Space complexity of reachability testing in labelled graphs
Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered s...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ramaswamy, Vidhya [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
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2019transfer abstract |
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14 |
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| Übergeordnetes Werk: |
Enthalten in: 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER - 2011, JCSS, San Diego, Calif. [u.a.] |
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| Übergeordnetes Werk: |
volume:105 ; year:2019 ; pages:40-53 ; extent:14 |
| Links: |
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| DOI / URN: |
10.1016/j.jcss.2019.04.002 |
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| Katalog-ID: |
ELV047241128 |
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| 100 | 1 | |a Ramaswamy, Vidhya |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Space complexity of reachability testing in labelled graphs |
| 264 | 1 | |c 2019transfer abstract | |
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| 520 | |a Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . | ||
| 520 | |a Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . | ||
| 650 | 7 | |a Algebraic reachability |2 Elsevier | |
| 650 | 7 | |a Dichotomy |2 Elsevier | |
| 650 | 7 | |a Space complexity |2 Elsevier | |
| 650 | 7 | |a Word problems |2 Elsevier | |
| 700 | 1 | |a Sarma, Jayalal |4 oth | |
| 700 | 1 | |a Sunil, K.S. |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |t 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER |d 2011 |d JCSS |g San Diego, Calif. [u.a.] |w (DE-627)ELV010661603 |
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10.1016/j.jcss.2019.04.002 doi GBV00000000000668.pica (DE-627)ELV047241128 (ELSEVIER)S0022-0000(18)30112-0 DE-627 ger DE-627 rakwb eng 610 VZ 570 540 VZ Ramaswamy, Vidhya verfasserin aut Space complexity of reachability testing in labelled graphs 2019transfer abstract 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Algebraic reachability Elsevier Dichotomy Elsevier Space complexity Elsevier Word problems Elsevier Sarma, Jayalal oth Sunil, K.S. oth Enthalten in Elsevier 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER 2011 JCSS San Diego, Calif. [u.a.] (DE-627)ELV010661603 volume:105 year:2019 pages:40-53 extent:14 https://doi.org/10.1016/j.jcss.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_39 GBV_ILN_62 GBV_ILN_90 GBV_ILN_120 GBV_ILN_127 GBV_ILN_227 GBV_ILN_2001 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2094 AR 105 2019 40-53 14 |
| spelling |
10.1016/j.jcss.2019.04.002 doi GBV00000000000668.pica (DE-627)ELV047241128 (ELSEVIER)S0022-0000(18)30112-0 DE-627 ger DE-627 rakwb eng 610 VZ 570 540 VZ Ramaswamy, Vidhya verfasserin aut Space complexity of reachability testing in labelled graphs 2019transfer abstract 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Algebraic reachability Elsevier Dichotomy Elsevier Space complexity Elsevier Word problems Elsevier Sarma, Jayalal oth Sunil, K.S. oth Enthalten in Elsevier 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER 2011 JCSS San Diego, Calif. [u.a.] (DE-627)ELV010661603 volume:105 year:2019 pages:40-53 extent:14 https://doi.org/10.1016/j.jcss.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_39 GBV_ILN_62 GBV_ILN_90 GBV_ILN_120 GBV_ILN_127 GBV_ILN_227 GBV_ILN_2001 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2094 AR 105 2019 40-53 14 |
| allfields_unstemmed |
10.1016/j.jcss.2019.04.002 doi GBV00000000000668.pica (DE-627)ELV047241128 (ELSEVIER)S0022-0000(18)30112-0 DE-627 ger DE-627 rakwb eng 610 VZ 570 540 VZ Ramaswamy, Vidhya verfasserin aut Space complexity of reachability testing in labelled graphs 2019transfer abstract 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Algebraic reachability Elsevier Dichotomy Elsevier Space complexity Elsevier Word problems Elsevier Sarma, Jayalal oth Sunil, K.S. oth Enthalten in Elsevier 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER 2011 JCSS San Diego, Calif. [u.a.] (DE-627)ELV010661603 volume:105 year:2019 pages:40-53 extent:14 https://doi.org/10.1016/j.jcss.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_39 GBV_ILN_62 GBV_ILN_90 GBV_ILN_120 GBV_ILN_127 GBV_ILN_227 GBV_ILN_2001 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2094 AR 105 2019 40-53 14 |
| allfieldsGer |
10.1016/j.jcss.2019.04.002 doi GBV00000000000668.pica (DE-627)ELV047241128 (ELSEVIER)S0022-0000(18)30112-0 DE-627 ger DE-627 rakwb eng 610 VZ 570 540 VZ Ramaswamy, Vidhya verfasserin aut Space complexity of reachability testing in labelled graphs 2019transfer abstract 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Algebraic reachability Elsevier Dichotomy Elsevier Space complexity Elsevier Word problems Elsevier Sarma, Jayalal oth Sunil, K.S. oth Enthalten in Elsevier 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER 2011 JCSS San Diego, Calif. [u.a.] (DE-627)ELV010661603 volume:105 year:2019 pages:40-53 extent:14 https://doi.org/10.1016/j.jcss.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_39 GBV_ILN_62 GBV_ILN_90 GBV_ILN_120 GBV_ILN_127 GBV_ILN_227 GBV_ILN_2001 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2094 AR 105 2019 40-53 14 |
| allfieldsSound |
10.1016/j.jcss.2019.04.002 doi GBV00000000000668.pica (DE-627)ELV047241128 (ELSEVIER)S0022-0000(18)30112-0 DE-627 ger DE-627 rakwb eng 610 VZ 570 540 VZ Ramaswamy, Vidhya verfasserin aut Space complexity of reachability testing in labelled graphs 2019transfer abstract 14 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . Algebraic reachability Elsevier Dichotomy Elsevier Space complexity Elsevier Word problems Elsevier Sarma, Jayalal oth Sunil, K.S. oth Enthalten in Elsevier 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER 2011 JCSS San Diego, Calif. [u.a.] (DE-627)ELV010661603 volume:105 year:2019 pages:40-53 extent:14 https://doi.org/10.1016/j.jcss.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_39 GBV_ILN_62 GBV_ILN_90 GBV_ILN_120 GBV_ILN_127 GBV_ILN_227 GBV_ILN_2001 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2094 AR 105 2019 40-53 14 |
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Enthalten in 1190 poster EVALUATION OF DEFORMABLE IMAGE CO-REGISTRATION IN ADAPTIVE IMRT FOR HEAD AND NECK CANCER San Diego, Calif. [u.a.] volume:105 year:2019 pages:40-53 extent:14 |
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Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . |
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Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . |
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Fix an algebraic structure ( A , ⁎ ) . Given a graph G = ( V , E ) and the labelling function ϕ ( ϕ : E → A ) for the edges, two nodes s, t ∈ V , and a subset F ⊆ A , the A -Reach problem asks if there is a path p (need not be simple) from s to t whose yield (result of the operation in the ordered set of the labels of the edges constituting the path) is in F. On the complexity frontier of this problem, we show the following results. • When A is a group whose size is polynomially bounded in the size of the graph (hence equivalently presented as a multiplication table at the input), and the graph is undirected, the A -Reach problem is in L . Building on this, using a decomposition in , we show that, when A is a fixed quasi-group, and the graph is undirected, the A -Reach problem is in L . In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. In contrast, we show that if the planar DAGs that we obtain above are bipartite, the problem can be further reduced to reachability testing in planar DAGs and hence is in UL . |
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In a contrast, we show NL -hardness of the problem over bidirected graphs, when A is a matrix group over Q , or an aperiodic monoid. • As our main theorem, we prove a dichotomy for graphs labelled with fixed aperiodic monoids by showing that for every fixed aperiodic monoid A , A -Reach problem is either in L or is NL -complete. • We show that there exists a monoid M, such that the reachability problem in general DAGs can be reduced to A -Reach problem for planar non-bipartite DAGs labelled with M. 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