Related papers: Breaking Value Symmetry
Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. In a recent series of papers, we have studied methods to break value symmetries. Our results…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…
We present a comprehensive study of the use of value precedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is both efficient and effective at breaking symmetry. We…
Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete,…
Without imposing restrictions on a weighted graph's arc lengths, symmetry structures cannot be expected. But, they exist. To find them, the graphs are decomposed into a component that dictates all closed path properties (e.g., shortest and…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
In their nature configuration problems are combinatorial (optimization) problems. In order to find a configuration a solver has to instantiate a number of components of a some type and each of these components can be used in a relation…
In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
In the context of Answer Set Programming, this paper investigates symmetry-breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We propose a reduction of disjunctive logic programs to a…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…