Related papers: Breaking Generator Symmetry
We construct real and complex matrices in terms of Kronecker products of a Witt basis of 2n null vectors in the geometric algebra over the real and complex numbers. In this basis, every matrix is represented by a unique sum of products of…
The computation of Gr\"obner bases is an established hard problem. By contrast with many other problems, however, there has been little investigation of whether this hardness is robust. In this paper, we frame and present results on the…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
Indistinguishable objects often occur when modelling problems in constraint programming, as well as in other related paradigms. They occur when objects can be viewed as being drawn from a set of unlabelled objects, and the only operation…
The pancake problem is concerned with sorting a permutation (a stack of pancakes of different diameter) using only prefix reversals (spatula flips). Although the problem description belies simplicity, an exact formula for the maximum number…
We study the problem of finding generators for the fundamental group G of a space of the following sort: one removes a family of complex hyperplanes from n dimensional complex vector space, or n dimensional complex hyperbolic space, or the…
When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…
We consider a fashion discounter that supplies any of its many branches with an integral multiple of lots whose size assortment structure stems from a set of many applicable lot-types. We design a column generation algorithm for the optimal…
In this paper we consider the problem of finding a vector that can be written as a nonnegative integer linear combination of given 0-1 vectors, the generators, such that the l_1-distance between this vector and a given target vector is…
This study examines the notion of generators of a pairwise comparisons matrix. Such approach decreases the number of pairwise comparisons from $n\cdot (n-1)$ to $n-1$. An algorithm of reconstructing of the PC matrix from its set of…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
We solve a supersymmetric matrix model with a general potential. While matrix models usually describe surfaces, supersymmetry enforces a cancellation of bosonic and fermionic loops and only diagrams corresponding to so-called branched…
Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such…
The task of scheduling jobs to machines while minimizing the total makespan, the sum of weighted completion times, or a norm of the load vector, are among the oldest and most fundamental tasks in combinatorial optimization. Since all of…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…