529 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Approximations for the Steiner Multicycle Problem
The Steiner Multicycle problem consists of, given a complete graph, a weight
function on its vertices, and a collection of pairwise disjoint non-unitary
sets called terminal sets, finding a minimum weight collection of
vertex-disjoint cycles in the graph such that, for every terminal set, all of
its vertices are in a same cycle of the collection. This problem generalizes
the Traveling Salesman problem and therefore is hard to approximate in general.
On the practical side, it models a collaborative less-than-truckload problem
with pickup and delivery locations. Using an algorithm for the Survivable
Network Design problem and T -joins, we obtain a 3-approximation for the metric
case, improving on the previous best 4-approximation. Furthermore, we present
an (11/9)-approximation for the particular case of the Steiner Multicycle in
which each edge weight is 1 or 2. This algorithm can be adapted to obtain a
(7/6)-approximation when every terminal set contains at least 4 vertices.
Finally, we devise an O(lg n)-approximation algorithm for the asymmetric
version of the problem
(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)
(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!
Proceedings of the 8th Workshop on Detection and Classification of Acoustic Scenes and Events (DCASE 2023)
This volume gathers the papers presented at the Detection and Classification of Acoustic Scenes and Events 2023 Workshop (DCASE2023), Tampere, Finland, during 21–22 September 2023
Learning Dynamic Priority Scheduling Policies with Graph Attention Networks
The aim of this thesis is to develop novel graph attention network-based models to automatically learn scheduling policies for effectively solving resource optimization problems, covering both deterministic and stochastic environments. The policy learning methods utilize both imitation learning, when expert demonstrations are accessible at low cost, and reinforcement learning, when otherwise reward engineering is feasible. By parameterizing the learner with graph attention networks, the framework is computationally efficient and results in scalable resource optimization schedulers that adapt to various problem structures. This thesis addresses the problem of multi-robot task allocation (MRTA) under temporospatial constraints. Initially, robots with deterministic and homogeneous task performance are considered with the development of the RoboGNN scheduler. Then, I develop ScheduleNet, a novel heterogeneous graph attention network model, to efficiently reason about coordinating teams of heterogeneous robots. Next, I address problems under the more challenging stochastic setting in two parts. Part 1) Scheduling with stochastic and dynamic task completion times. The MRTA problem is extended by introducing human coworkers with dynamic learning curves and stochastic task execution. HybridNet, a hybrid network structure, has been developed that utilizes a heterogeneous graph-based encoder and a recurrent schedule propagator, to carry out fast schedule generation in multi-round settings. Part 2) Scheduling with stochastic and dynamic task arrival and completion times. With an application in failure-predictive plane maintenance, I develop a heterogeneous graph-based policy optimization (HetGPO) approach to enable learning robust scheduling policies in highly stochastic environments. Through extensive experiments, the proposed framework has been shown to outperform prior state-of-the-art algorithms in different applications. My research contributes several key innovations regarding designing graph-based learning algorithms in operations research.Ph.D
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning
The paper introduces the application of information geometry to describe the
ground states of Ising models by utilizing parity-check matrices of cyclic and
quasi-cyclic codes on toric and spherical topologies. The approach establishes
a connection between machine learning and error-correcting coding. This
proposed approach has implications for the development of new embedding methods
based on trapping sets. Statistical physics and number geometry applied for
optimize error-correcting codes, leading to these embedding and sparse
factorization methods. The paper establishes a direct connection between DNN
architecture and error-correcting coding by demonstrating how state-of-the-art
architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range
arena can be equivalent to of block and convolutional LDPC codes (Cage-graph,
Repeat Accumulate). QC codes correspond to certain types of chemical elements,
with the carbon element being represented by the mixed automorphism
Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and
the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix
are elaborated upon in detail. The Quantum Approximate Optimization Algorithm
(QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous
to the back-propagation loss function landscape in training DNNs. This
similarity creates a comparable problem with TS pseudo-codeword, resembling the
belief propagation method. Additionally, the layer depth in QAOA correlates to
the number of decoding belief propagation iterations in the Wiberg decoding
tree. Overall, this work has the potential to advance multiple fields, from
Information Theory, DNN architecture design (sparse and structured prior graph
topology), efficient hardware design for Quantum and Classical DPU/TPU (graph,
quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text
overlap with arXiv:2109.08184 by other author
Graph Learning and Its Applications: A Holistic Survey
Graph learning is a prevalent domain that endeavors to learn the intricate
relationships among nodes and the topological structure of graphs. These
relationships endow graphs with uniqueness compared to conventional tabular
data, as nodes rely on non-Euclidean space and encompass rich information to
exploit. Over the years, graph learning has transcended from graph theory to
graph data mining. With the advent of representation learning, it has attained
remarkable performance in diverse scenarios, including text, image, chemistry,
and biology. Owing to its extensive application prospects, graph learning
attracts copious attention from the academic community. Despite numerous works
proposed to tackle different problems in graph learning, there is a demand to
survey previous valuable works. While some researchers have perceived this
phenomenon and accomplished impressive surveys on graph learning, they failed
to connect related objectives, methods, and applications in a more coherent
way. As a result, they did not encompass current ample scenarios and
challenging problems due to the rapid expansion of graph learning. Different
from previous surveys on graph learning, we provide a holistic review that
analyzes current works from the perspective of graph structure, and discusses
the latest applications, trends, and challenges in graph learning.
Specifically, we commence by proposing a taxonomy from the perspective of the
composition of graph data and then summarize the methods employed in graph
learning. We then provide a detailed elucidation of mainstream applications.
Finally, based on the current trend of techniques, we propose future
directions.Comment: 20 pages, 7 figures, 3 table
Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities
Decision-focused learning (DFL) is an emerging paradigm in machine learning
which trains a model to optimize decisions, integrating prediction and
optimization in an end-to-end system. This paradigm holds the promise to
revolutionize decision-making in many real-world applications which operate
under uncertainty, where the estimation of unknown parameters within these
decision models often becomes a substantial roadblock. This paper presents a
comprehensive review of DFL. It provides an in-depth analysis of the various
techniques devised to integrate machine learning and optimization models,
introduces a taxonomy of DFL methods distinguished by their unique
characteristics, and conducts an extensive empirical evaluation of these
methods proposing suitable benchmark dataset and tasks for DFL. Finally, the
study provides valuable insights into current and potential future avenues in
DFL research.Comment: Experimental Survey and Benchmarkin
Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization
Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes
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