The SAT modulo Symmetries (SMS) is a recently introduced framework for dynamic symmetry breaking in SAT instances. It combines a CDCL SAT solver with an external lexicographic minimality checking algorithm. We extend ...
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We investigate two optimization problems on area-proportional rectangle contact representations for layered, embedded planar graphs. The vertices are represented as interior-disjoint unit-height rectangles of prescrib...
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Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via cross...
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Hedonic diversity games are a variant of the classical Hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classe...
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In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when deali...
In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions. Indeed, while there has been a number of very recent results that establish ever-tighter lower bounds for the problem under linear and ReLU activation functions, less progress has been made towards the identification of novel polynomial-time tractable network architectures. In this article we obtain novel algorithmic upper bounds for training linear- and ReLU-activated neural networks to optimality which push the boundaries of tractability for these problems beyond the previous state of the art. In particular, for ReLU networks we establish the polynomial-time tractability of all architectures where hidden neurons have an out-degree of 1, improving upon the previous algorithm of Arora, Basu, Mianjy and Mukherjee. On the other hand, for networks with linear activation functions we identify the first non-trivial polynomial-time solvable class of networks by obtaining an algorithm that can optimally train network architectures satisfying a novel data throughput condition.
The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research ar...
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In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly 90◦, where the number of bends on such polylines is typically restricted ...
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In public transport networks disruptions may occur and lead to travel delays. It is thus interesting to determine whether a traveler can be resilient to delays that occur unexpectedly, ensuring that they can reach the...
For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall...
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Map labeling is a classical problem in cartography and geographic information systems that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent (...
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Map labeling is a classical problem in cartography and geographic information systems that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent (i.e., overlap-free) labels. A practically interesting case is point labeling with axis-parallel rectangular labels of common size. In a fully dynamic setting, at each timestep, either a new label appears or an existing label disappears. Then, the challenge is to maintain a maximum cardinality subset of pairwise independent labels with sublinear update time. Motivated by this, we study the maximal independent set (MIS) and maximum independent set (Max-IS) problems on fully dynamic (insertion/deletion model) sets of axis-parallel rectangles of two types: (i) uniform height and width and (ii) uniform height and arbitrary width;both settings can be modeled as rectangle intersection graphs. We present the first deterministic algorithm for maintaining an MIS (and thus a 4-approximate Max-IS) of a dynamic set of uniform rectangles with polylogarithmic update time. This breaks the natural barrier of update time (where is the maximum degree in the graph) for vertex updates presented by Assadi et al. (STOC 2018). We continue by investigating Max-IS and provide a series of deterministic dynamic approximation schemes. For uniform rectangles, we first give an algorithm that maintains a 4-approximate Max-IS with update time. In a subsequent algorithm, we establish the trade-off between approximation quality and update time , for . We conclude with an algorithm that maintains a 2-approximate Max-IS for dynamic sets of unit-height and arbitrary-width rectangles with update time, where is the maximum size of an independent set of rectangles stabbed by any horizontal line. We implement our algorithms and report the results of an experimental comparison exploring the trade-off between solution quality and update time for synthetic and real-world map labeling instances. We
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