Related papers: Optimal antimatroid sorting
We consider the problem of sorting $n$ elements subject to persistent random comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability $p$, and comparing the same pair of…
We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…
When dealing with massive data sorting, we usually use Hadoop which is a framework that allows for the distributed processing of large data sets across clusters of computers using simple programming models. A common approach in implement of…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…
We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…
We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…
In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved…
While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly…
The generalized list $T$-coloring is a common generalization of many graph coloring models, including classical coloring, $L(p,q)$-labeling, channel assignment and $T$-coloring. Every vertex from the input graph has a list of permitted…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…
State-of-the-art parallel sorting algorithms for distributed-memory architectures are based on computing a balanced partitioning via sampling and histogramming. By finding samples that partition the sorted keys into evenly-sized chunks,…
Dominating set problems are among the most important class of combinatorial problems in graph optimization, from a theoretical as well as from a practical point of view. In this paper, we address the recently introduced (minimum) weighted…
Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…
We present one stable mergesort algorithm, called \Adaptive Shivers Sort, that exploits the existence of monotonic runs for sorting efficiently partially sorted data. We also prove that, although this algorithm is simple to implement, its…
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…
Two seemingly unrelated problems, scheduling a multiclass queueing system and minimizing a submodular function, share a rather deep connection via the polymatroid that is characterized by a submodular set function on the one hand and…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
We modify the Pearce-Kelly algorithm that maintains a topological ordering for a directed acyclic graph in order to allow cycles to be tolerated. Cycles make topological orderings moot, of course, however tolerating them is useful in…