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Symmetry Breaking in Graphs
 Electronic Journal of Combinatorics
, 1996
"... A labeling of the vertices of a graph G, OE : V (G) ! f1; : : : ; rg, is said to be rdistinguishing provided no automorphism of the graph preserves all of the vertex labels. The distinguishing number of a graph G, denoted by D(G), is the minimum r such that G has an rdistinguishing labeling. T ..."
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Cited by 34 (4 self)
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A labeling of the vertices of a graph G, OE : V (G) ! f1; : : : ; rg, is said to be rdistinguishing provided no automorphism of the graph preserves all of the vertex labels. The distinguishing number of a graph G, denoted by D(G), is the minimum r such that G has an rdistinguishing labeling
Symmetry Breaking Ordering Constraints
, 2004
"... In a constraint satisfaction problem (CSP), symmetry involves the variables, values in the domains, or both, and maps each search state into an equivalent one. When searching for solutions, symmetrically equivalent (partial) assignments can dramatically increase the search space. Hence, elimination ..."
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Cited by 14 (3 self)
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In a constraint satisfaction problem (CSP), symmetry involves the variables, values in the domains, or both, and maps each search state into an equivalent one. When searching for solutions, symmetrically equivalent (partial) assignments can dramatically increase the search space. Hence, elimination
Gauge Symmetry Breaking in Models
, 1999
"... In models inspired by noncommutative geometry, patterns of gauge symmetry breaking are analyzed, and SU(5) models are found to favor a vacuum preserving SU(3)C × SU(2)W × U(1)Y naturally. A setup for a more realistic model is presented, and a possibility of Dbrane interpretation is discussed. ..."
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In models inspired by noncommutative geometry, patterns of gauge symmetry breaking are analyzed, and SU(5) models are found to favor a vacuum preserving SU(3)C × SU(2)W × U(1)Y naturally. A setup for a more realistic model is presented, and a possibility of Dbrane interpretation is discussed.
Symmetry Breaking in Soft CSPs
 IN RESEARCH AND DEVELOPMENT IN INTELLIGENT SYSTEMS XX, PROCEEDINGS OF AI2003, THE TWENTYTHIRD SGAI INTERNATIONAL CONFERENCE ON KNOWLEDGEBASED SYSTEMS AND APPLIED ARTIFICIAL INTELLIGENCE, VOLUME RESEARCH AND DEVELOPMENT IN INTELLIGENT SYSTEMS XX OF BCS C
, 2003
"... Exploiting symmetry in constraint satisfaction problems has become a very popular topic of research in recent times. The existence of symmetry in a problem has the effect of artificially increasing the size of the search space that is explored by search algorithms. Another significant topic of r ..."
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Cited by 3 (3 self)
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Exploiting symmetry in constraint satisfaction problems has become a very popular topic of research in recent times. The existence of symmetry in a problem has the effect of artificially increasing the size of the search space that is explored by search algorithms. Another significant topic
Lightweight Dynamic Symmetry Breaking
"... LDSB is a dynamic symmetry breaking method and, therefore, it does not interfere with the given search heuristic. Like the shortcut SBDS method, it might trade completeness for efficiency, and does not require complex group theory computations. Like the GAPSBDS method, it only requires the user to ..."
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Cited by 1 (0 self)
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LDSB is a dynamic symmetry breaking method and, therefore, it does not interfere with the given search heuristic. Like the shortcut SBDS method, it might trade completeness for efficiency, and does not require complex group theory computations. Like the GAPSBDS method, it only requires the user
Groups, graphs and symmetrybreaking
, 1998
"... A labeling of a graph G is said to be rdistinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an rdistinguishing labeling on G is called the distinguishing number of G. Thedistinguishing set of a group Γ, D(Γ), is the set of distin ..."
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Cited by 1 (0 self)
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A labeling of a graph G is said to be rdistinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an rdistinguishing labeling on G is called the distinguishing number of G. Thedistinguishing set of a group Γ, D(Γ), is the set
Study: Symmetry breaking
"... The configuration problem consists in finding a sequence of actions required to assemble a target artifact from a set of components of predefined types. All allowed components types, their attributes and possible relations between components are specified as configuration constraints. In addition, ..."
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The configuration problem consists in finding a sequence of actions required to assemble a target artifact from a set of components of predefined types. All allowed components types, their attributes and possible relations between components are specified as configuration constraints. In addition,
Symmetry Breaking During Drosophila
"... The orthogonal axes of Drosophila are established during oogenesis through a hierarchical series of symmetrybreaking steps, most of which can be traced back to asymmetries inherent in the architecture of the ovary. Oogenesis begins with the formation of a germline cyst of 16 cells connected by rin ..."
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establishes the posterior cortex of the oocyte. The next two steps of symmetry breaking occur during midoogenesis after the volume of the oocyte has increased about 10fold. First, a signal from the oocyte specifies posterior follicle cells, polarizing a symmetric prepattern present within the follicular
An introduction to SYMMETRY BREAKING IN GRAPHS
"... This is intended to be a short summary of results that will appear elsewhere, with the goal being to reach the list of open problems at the end. Our motivation is the following: Professor X has a key ring with n seemingly identical keys (that open different doors). We put colored labels on the keys ..."
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to distinguish them. What is the minimum number of colors needed? This first appeared in [3], and was brought to our attention by S. Wagon [2]. It translates to the following graph labeling problem: What is the minimum number of colors needed to label the vertices of Cn so that no automorphism of Cn preserves
An introduction to SYMMETRY BREAKING IN GRAPHS
"... This is intended to be a short summary of results that will appear elsewhere, with the goal being to reach the list of open problems at the end. Our motivation is the following: Professor X has a key ring with n seemingly identical keys (that open dierent doors). We put colored labels on the keys t ..."
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preserves the labeling? The surprise is that three colors are needed if n = 3; 4; 5, but for n 6, two colors suÆce. LetG be a graph with vertex set V. We dene an rdistinguishing labeling to be a map : V! f1; 2; 3; : : : ; rg such that for any nontrivial automorphism of G, there exists vertex u
Results 1  10
of
1,127