6,634 research outputs found
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Algorithms and complexity for approximately counting hypergraph colourings and related problems
The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of Lovász local lemma when Δ ≲ qᵏ. In prior, however, fast approximate counting algorithms exist when Δ ≲ qᵏ/³, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows.
• When q, k ≥ 4 are evens and Δ ≥ 5·qᵏ/², approximating the number of hypergraph colourings is NP-hard.
• When the input hypergraph is linear and Δ ≲ qᵏ/², a fast approximate counting algorithm does exist
Conversations on Empathy
In the aftermath of a global pandemic, amidst new and ongoing wars, genocide, inequality, and staggering ecological collapse, some in the public and political arena have argued that we are in desperate need of greater empathy — be this with our neighbours, refugees, war victims, the vulnerable or disappearing animal and plant species. This interdisciplinary volume asks the crucial questions: How does a better understanding of empathy contribute, if at all, to our understanding of others? How is it implicated in the ways we perceive, understand and constitute others as subjects? Conversations on Empathy examines how empathy might be enacted and experienced either as a way to highlight forms of otherness or, instead, to overcome what might otherwise appear to be irreducible differences. It explores the ways in which empathy enables us to understand, imagine and create sameness and otherness in our everyday intersubjective encounters focusing on a varied range of "radical others" – others who are perceived as being dramatically different from oneself. With a focus on the importance of empathy to understand difference, the book contends that the role of empathy is critical, now more than ever, for thinking about local and global challenges of interconnectedness, care and justice
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Witnessing environment dimension through temporal correlations
We introduce a framework to compute upper bounds for temporal correlations
achievable in open quantum system dynamics, obtained by repeated measurements
on the system. As these correlations arise by virtue of the environment acting
as a memory resource, such bounds are witnesses for the minimal dimension of an
effective environment compatible with the observed statistics. These witnesses
are derived from a hierarchy of semidefinite programs with guaranteed
asymptotic convergence. We compute non-trivial bounds for various sequences
involving a qubit system and a qubit environment, and compare the results to
the best known quantum strategies producing the same outcome sequences. Our
results provide a numerically tractable method to determine bounds on
multi-time probability distributions in open quantum system dynamics and allow
for the witnessing of effective environment dimensions through probing of the
system alone.Comment: 24 pages, 7 figure
Maximizing Neutrality in News Ordering
The detection of fake news has received increasing attention over the past
few years, but there are more subtle ways of deceiving one's audience. In
addition to the content of news stories, their presentation can also be made
misleading or biased. In this work, we study the impact of the ordering of news
stories on audience perception. We introduce the problems of detecting
cherry-picked news orderings and maximizing neutrality in news orderings. We
prove hardness results and present several algorithms for approximately solving
these problems. Furthermore, we provide extensive experimental results and
present evidence of potential cherry-picking in the real world.Comment: 14 pages, 13 figures, accepted to KDD '2
Towards a centralized multicore automotive system
Today’s automotive systems are inundated with embedded electronics to host chassis, powertrain, infotainment, advanced driver assistance systems, and other modern vehicle functions. As many as 100 embedded microcontrollers execute hundreds of millions of lines of code in a single vehicle. To control the increasing complexity in vehicle electronics and services, automakers are planning to consolidate different on-board automotive functions as software tasks on centralized multicore hardware platforms. However, these vehicle software services have different and contrasting timing, safety, and security requirements. Existing vehicle operating systems are ill-equipped to provide all the required service guarantees on a single machine. A centralized automotive system aims to tackle this by assigning software tasks to multiple criticality domains or levels according to their consequences of failures, or international safety standards like ISO 26262. This research investigates several emerging challenges in time-critical systems for a centralized multicore automotive platform and proposes a novel vehicle operating system framework to address them.
This thesis first introduces an integrated vehicle management system (VMS), called DriveOS™, for a PC-class multicore hardware platform. Its separation kernel design enables temporal and spatial isolation among critical and non-critical vehicle services in different domains on the same machine. Time- and safety-critical vehicle functions are implemented in a sandboxed Real-time Operating System (OS) domain, and non-critical software is developed in a sandboxed general-purpose OS (e.g., Linux, Android) domain. To leverage the advantages of model-driven vehicle function development, DriveOS provides a multi-domain application framework in Simulink. This thesis also presents a real-time task pipeline scheduling algorithm in multiprocessors for communication between connected vehicle services with end-to-end guarantees. The benefits and performance of the overall automotive system framework are demonstrated with hardware-in-the-loop testing using real-world applications, car datasets and simulated benchmarks, and with an early-stage deployment in a production-grade luxury electric vehicle
Improved Approximations for Translational Packing of Convex Polygons
Optimal packing of objects in containers is a critical problem in various
real-life and industrial applications. This paper investigates the
two-dimensional packing of convex polygons without rotations, where only
translations are allowed. We study different settings depending on the type of
containers used, including minimizing the number of containers or the size of
the container based on an objective function.
Building on prior research in the field, we develop polynomial-time
algorithms with improved approximation guarantees upon the best-known results
by Alt, de Berg and Knauer, as well as Aamand, Abrahamsen, Beretta and Kleist,
for problems such as Polygon Area Minimization, Polygon Perimeter Minimization,
Polygon Strip Packing, and Polygon Bin Packing. Our approach utilizes a
sequence of object transformations that allows sorting by height and
orientation, thus enhancing the effectiveness of shelf packing algorithms for
polygon packing problems. In addition, we present efficient approximation
algorithms for special cases of the Polygon Bin Packing problem, progressing
toward solving an open question concerning an O(1)-approximation algorithm for
arbitrary polygons.Comment: This is the full version of the same-named paper which will be
presented at ESA 2023 conferenc
Improved Approximation Algorithms for Steiner Connectivity Augmentation Problems
The Weighted Connectivity Augmentation Problem is the problem of augmenting
the edge-connectivity of a given graph by adding links of minimum total cost.
This work focuses on connectivity augmentation problems in the Steiner setting,
where we are not interested in the connectivity between all nodes of the graph,
but only the connectivity between a specified subset of terminals.
We consider two related settings. In the Steiner Augmentation of a Graph
problem (-SAG), we are given a -edge-connected subgraph of a graph
. The goal is to augment by including links and nodes from of
minimum cost so that the edge-connectivity between nodes of increases by 1.
In the Steiner Connectivity Augmentation Problem (-SCAP), we are given a
Steiner -edge-connected graph connecting terminals , and we seek to add
links of minimum cost to create a Steiner -edge-connected graph for .
Note that -SAG is a special case of -SCAP.
All of the above problems can be approximated to within a factor of 2 using
e.g. Jain's iterative rounding algorithm for Survivable Network Design. In this
work, we leverage the framework of Traub and Zenklusen to give a -approximation for the Steiner Ring Augmentation Problem (SRAP):
given a cycle embedded in a larger graph and
a subset of terminals , choose a subset of links of minimum cost so that has 3 pairwise edge-disjoint paths
between every pair of terminals.
We show this yields a polynomial time algorithm with approximation ratio for -SCAP. We obtain an improved approximation
guarantee of for SRAP in the case that , which
yields a -approximation for -SAG for any
- …