Related papers: Partial order alignment by adjacencies and breakpo…

Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…

We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…

Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless…

This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a…

Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it…

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…

We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper…

The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…

We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…

We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection between partial matchings avoiding three…

We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…

Software is now ubiquitous and involved in complex interactions with the human users and the physical world in so-called cyber-physical systems where the management of time is a major issue. Separation of concerns is a key asset in the…

We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…

The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important…

This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they…

Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order…