IA Scholar Query: Fast maximum clique algorithms for large graphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 31 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Computing Graph Neural Networks: A Survey from Algorithms to Accelerators
https://scholar.archive.org/work/7uww2lnxrbdpnnyvzsanojgnba
Graph Neural Networks (GNNs) have exploded onto the machine learning scene in recent years owing to their capability to model and learn from graph-structured data. Such an ability has strong implications in a wide variety of fields whose data are inherently relational, for which conventional neural networks do not perform well. Indeed, as recent reviews can attest, research in the area of GNNs has grown rapidly and has lead to the development of a variety of GNN algorithm variants as well as to the exploration of ground-breaking applications in chemistry, neurology, electronics, or communication networks, among others. At the current stage research, however, the efficient processing of GNNs is still an open challenge for several reasons. Besides of their novelty, GNNs are hard to compute due to their dependence on the input graph, their combination of dense and very sparse operations, or the need to scale to huge graphs in some applications. In this context, this article aims to make two main contributions. On the one hand, a review of the field of GNNs is presented from the perspective of computing. This includes a brief tutorial on the GNN fundamentals, an overview of the evolution of the field in the last decade, and a summary of operations carried out in the multiple phases of different GNN algorithm variants. On the other hand, an in-depth analysis of current software and hardware acceleration schemes is provided, from which a hardware-software, graph-aware, and communication-centric vision for GNN accelerators is distilled.Sergi Abadal, Akshay Jain, Robert Guirado, Jorge López-Alonso, Eduard Alarcónwork_7uww2lnxrbdpnnyvzsanojgnbaSat, 31 Dec 2022 00:00:00 GMTAn Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling
https://scholar.archive.org/work/by4kwstrpzgk3fvpxqnu3yoeiq
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 \( \Omega (\Delta) \) update time (where \( \Delta \) 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 \( O(1) \) update time. In a subsequent algorithm, we establish the trade-off between approximation quality \( 2(1+\frac{1}{k}) \) and update time \( O(k^2\log n) \) , for \( k\in \mathbb {N} \) . We conclude with an algorithm that maintains a 2-approximate Max-IS for dynamic sets of unit-height and arbitrary-width rectangles with \( O(\log ^2 n + \omega \log n) \) update time, where \( \omega \) 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 made several major observations in our empirical study. First, the original approximations are well above their respective worst-case ratios. Second, in comparison with the static approaches, the dynamic approaches show a significant speedup in practice. Third, the approximation algorithms show their predicted relative behavior. The better the solution quality, the worse the update times. Fourth, a simple greedy augmentation to the approximate solutions of the algorithms boost the solution sizes significantly in practice.Sujoy Bhore, Guangping Li, Martin Nöllenburgwork_by4kwstrpzgk3fvpxqnu3yoeiqSat, 31 Dec 2022 00:00:00 GMTDescriptive Combinatorics and Distributed Algorithms
https://scholar.archive.org/work/pjgjlnfrkzd5vmd7p7c5yr66pe
In this article we shall explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed algorithms-a fundamental part of computer science that is becoming increasingly important in the modern era of decentralized computation. The interdisciplinary nature of these connections means that there is very little common background shared by the researchers who are interested in them. With this in mind, this article was written under the assumption that the reader would have close to no background in either descriptive set theory or computer science. The reader will judge to what degree this endeavor was successful. The article comprises two parts. In the first part we give a brief introduction to some of the central notions and problems of descriptive combinatorics. The second part is devoted to a survey of some of the results concerning theAnton Bernshteynwork_pjgjlnfrkzd5vmd7p7c5yr66peSat, 01 Oct 2022 00:00:00 GMTMining on Alzheimer's diseases related knowledge graph to identity potential AD-related semantic triples for drug repurposing
https://scholar.archive.org/work/gdsvz7oxrfewhegpivw6g7o6be
To date, there are no effective treatments for most neurodegenerative diseases. Knowledge graphs can provide comprehensive and semantic representation for heterogeneous data, and have been successfully leveraged in many biomedical applications including drug repurposing. Our objective is to construct a knowledge graph from literature to study the relations between Alzheimer's disease (AD) and chemicals, drugs and dietary supplements in order to identify opportunities to prevent or delay neurodegenerative progression. We collected biomedical annotations and extracted their relations using SemRep via SemMedDB. We used both a BERT-based classifier and rule-based methods during data preprocessing to exclude noise while preserving most AD-related semantic triples. The 1,672,110 filtered triples were used to train with knowledge graph completion algorithms (i.e., TransE, DistMult, and ComplEx) to predict candidates that might be helpful for AD treatment or prevention. Among three knowledge graph completion models, TransE outperformed the other two (MR = 10.53, Hits@1 = 0.28). We leveraged the time-slicing technique to further evaluate the prediction results. We found supporting evidence for most highly ranked candidates predicted by our model which indicates that our approach can inform reliable new knowledge. This paper shows that our graph mining model can predict reliable new relationships between AD and other entities (i.e., dietary supplements, chemicals, and drugs). The knowledge graph constructed can facilitate data-driven knowledge discoveries and the generation of novel hypotheses.Yi Nian, Xinyue Hu, Rui Zhang, Jingna Feng, Jingcheng Du, Fang Li, Larry Bu, Yuji Zhang, Yong Chen, Cui Taowork_gdsvz7oxrfewhegpivw6g7o6beFri, 30 Sep 2022 00:00:00 GMTSmall protein complex prediction algorithm based on protein-protein interaction network segmentation
https://scholar.archive.org/work/7dm5ls53s5auhhkagrl7dakj4a
Identifying protein complexes from protein-protein interaction network is one of significant tasks in the postgenome era. Protein complexes, none of which exceeds 10 in size play an irreplaceable role in life activities and are also a hotspot of scientific research, such as PSD-95, CD44, PKM2 and BRD4. And in MIPS, CYC2008, SGD, Aloy and TAP06 datasets, the proportion of small protein complexes is over 75%. But up to now, protein complex identification methods do not perform well in the field of small protein complexes. In this paper, we propose a novel method, called BOPS. It is a three-step procedure. Firstly, it calculates the balanced weights to replace the original weights. Secondly, it divides the graphs larger than MAXP until the original PPIN is divided into small PPINs. Thirdly, it enumerates the connected subset of each small PPINs, identifies potential protein complexes based on cohesion and removes those that are similar. In four yeast PPINs, experimental results have shown that BOPS has an improvement of about 5% compared with the SOTA model. In addition, we constructed a weighted Homo sapiens PPIN based on STRINGdb and BioGRID, and BOPS gets the best result in it. These results give new insights into the identification of small protein complexes, and the weighted Homo sapiens PPIN provides more data for related research.Jiaqing Lyu, Zhen Yao, Bing Liang, Yiwei Liu, Yijia Zhangwork_7dm5ls53s5auhhkagrl7dakj4aFri, 30 Sep 2022 00:00:00 GMTRTX-KG2: a system for building a semantically standardized knowledge graph for translational biomedicine
https://scholar.archive.org/work/ecfsauwx2zfdrjqh6va2ea3hnm
Biomedical translational science is increasingly using computational reasoning on repositories of structured knowledge (such as UMLS, SemMedDB, ChEMBL, Reactome, DrugBank, and SMPDB in order to facilitate discovery of new therapeutic targets and modalities. The NCATS Biomedical Data Translator project is working to federate autonomous reasoning agents and knowledge providers within a distributed system for answering translational questions. Within that project and the broader field, there is a need for a framework that can efficiently and reproducibly build an integrated, standards-compliant, and comprehensive biomedical knowledge graph that can be downloaded in standard serialized form or queried via a public application programming interface (API). To create a knowledge provider system within the Translator project, we have developed RTX-KG2, an open-source software system for building-and hosting a web API for querying-a biomedical knowledge graph that uses an Extract-Transform-Load approach to integrate 70 knowledge sources (including the aforementioned core six sources) into a knowledge graph with provenance information including (where available) citations. The semantic layer and schema for RTX-KG2 follow the standard Biolink model to maximize interoperability. RTX-KG2 is currently being used by multiple Translator reasoning agents, both in its downloadable form and via its SmartAPI-registered interface. Serializations of RTX-KG2 are available for download in both the pre-canonicalized form and in canonicalized form (in which synonyms are merged). The current canonicalized version (KG2.7.3) of RTX-KG2 contains 6.4M nodes and 39.3M edges with a hierarchy of 77 relationship types from Biolink. RTX-KG2 is the first knowledge graph that integrates UMLS, SemMedDB, ChEMBL, DrugBank, Reactome, SMPDB, and 64 additional knowledge sources within a knowledge graph that conforms to the Biolink standard for its semantic layer and schema. RTX-KG2 is publicly available for querying via its API at arax.rtx.ai/api/rtxkg2/v1.2/openapi.json . The code to build RTX-KG2 is publicly available at github:RTXteam/RTX-KG2 .E C Wood, Amy K Glen, Lindsey G Kvarfordt, Finn Womack, Liliana Acevedo, Timothy S Yoon, Chunyu Ma, Veronica Flores, Meghamala Sinha, Yodsawalai Chodpathumwan, Arash Termehchy, Jared C Roach, Luis Mendoza, Andrew S Hoffman, Eric W Deutsch, David Koslicki, Stephen A Ramseywork_ecfsauwx2zfdrjqh6va2ea3hnmThu, 29 Sep 2022 00:00:00 GMTA Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption
https://scholar.archive.org/work/vlqa6rnsa5d3vnpa3qeaizot6a
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in the same way. 2. The computational aspects of lattice-based cryptosystem are usually simple to understand and fairly easy to implement in practice. 3. Lattice-based cryptosystems have lower encryption/decryption computational complexities compared to popular cryptosystems that are based on the integer factorisation or the discrete logarithm problems. 4. Lattice-based cryptosystems enjoy strong worst-case hardness security proofs based on approximate versions of known NP-hard lattice problems. 5. Lattice-based cryptosystems are believed to be good candidates for post-quantum cryptography, since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best-known classical (non-quantum) algorithms, unlike for integer factorisation and (elliptic curve) discrete logarithm problems. 6. Last but not least, interesting structures in lattice problems have led to significant advances in Homomorphic Encryption, a new research area with wide-ranging applications.Yang Li, Kee Siong Ng, Michael Purcellwork_vlqa6rnsa5d3vnpa3qeaizot6aWed, 28 Sep 2022 00:00:00 GMTEfficient parameterized algorithms on graphs with heterogeneous structure: Combining tree-depth and modular-width
https://scholar.archive.org/work/cv5h74p5anawpkkaqte2xz7bga
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small modular-width or small tree-width, than on general graphs. One challenge is to attain the greatest generality of such results, i.e., being applicable to less restrictive input classes, without losing much in terms of running time. Building on the use of algebraic expressions we present a clean and robust way of combining such homogeneous structure into more complex heterogeneous structure, and we show-case this for the combination of modular-width, tree-depth, and a natural notion of modular tree-depth. We give a generic framework for designing efficient parameterized algorithms on the created graph classes, aimed at getting competitive running times that match the homogeneous cases. To show the applicability we give efficient parameterized algorithms for Negative Cycle Detection, Vertex-Weighted All-Pairs Shortest Paths, and Triangle Counting.Stefan Kratsch, Florian Nelleswork_cv5h74p5anawpkkaqte2xz7bgaWed, 28 Sep 2022 00:00:00 GMTEvaluating Hybrid Graph Pattern Queries Using Runtime Index Graphs
https://scholar.archive.org/work/wpedltg7dncw3lpwplbnugmeja
Graph pattern matching is a fundamental operation for the analysis and exploration ofdata graphs. In thispaper, we presenta novel approachfor efficiently finding homomorphic matches for hybrid graph patterns, where each pattern edge may be mapped either to an edge or to a path in the input data, thus allowing for higher expressiveness and flexibility in query formulation. A key component of our approach is a lightweight index structure that leverages graph simulation to compactly encode the query answer search space. The index can be built on-the-fly during query execution and does not have to be persisted to disk. Using the index, we design a multi-way join algorithm to enumerate query solutions without generating any potentially exploding intermediate results. We demonstrate through extensive experiments that our approach can efficiently evaluate a wide range / broad spectrum of graph pattern queries and greatly outperforms existing approaches and recent graph query engines/systems.Xiaoying Wu and Dimitri Theodoratos and Nikos Mamoulis and Michael Lanwork_wpedltg7dncw3lpwplbnugmejaWed, 28 Sep 2022 00:00:00 GMTRobust Incremental Smoothing and Mapping (riSAM)
https://scholar.archive.org/work/ckgrfyh6jzhbbnzyjcehqy3d4q
This paper presents a method for robust optimization for online incremental Simultaneous Localization and Mapping (SLAM). Due to the NP-Hardness of data association in the presence of perceptual aliasing, tractable (approximate) approaches to data association will produce erroneous measurements. We require SLAM back-ends that can converge to accurate solutions in the presence of outlier measurements while meeting online efficiency constraints. Existing robust SLAM methods either remain sensitive to outliers, become increasingly sensitive to initialization, or fail to provide online efficiency. We present the robust incremental Smoothing and Mapping (riSAM) algorithm, a robust back-end optimizer for incremental SLAM based on Graduated Non-Convexity. We demonstrate on benchmarking datasets that our algorithm achieves online efficiency, outperforms existing online approaches, and matches or improves the performance of existing offline methods.Daniel McGann, John G. Rogers III, Michael Kaesswork_ckgrfyh6jzhbbnzyjcehqy3d4qWed, 28 Sep 2022 00:00:00 GMTORKA: Object reconstruction using a K-approximation graph
https://scholar.archive.org/work/ogehrahojjczhhpiz3us7lak5a
Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these problems, it is often assumed that the data is sparse or low-dimensional in some domain. When multiple measurements are taken, this sparsity often appears in a structured manner. We propose a new model that assumes the data only contains a few relevant objects, i.e., it is sparse in some object domain. We model an object as a structure that can only change slightly in form and continuously in position over different measurements. This can be modeled by a matrix with highly correlated columns and a column shift operator that we introduce in this work. We present an efficient algorithm to solve the object reconstruction problem based on a K-approximation graph. We prove optimal approximation bounds and perform a numerical evaluation of the method. Examples from applications including Geophysics, video processing, and others will be given.Florian Bossmann, Jianwei Mawork_ogehrahojjczhhpiz3us7lak5aTue, 27 Sep 2022 00:00:00 GMTCalculating the Moore–Penrose Generalized Inverse on Massively Parallel Systems
https://scholar.archive.org/work/xza5krlk2ngyhc3hwxuiikbs2q
In this work, we consider the problem of calculating the generalized Moore–Penrose inverse, which is essential in many applications of graph theory. We propose an algorithm for the massively parallel systems based on the recursive algorithm for the generalized Moore–Penrose inverse, the generalized Cholesky factorization, and Strassen's matrix inversion algorithm. Computational experiments with our new algorithm based on a parallel computing architecture known as the Compute Unified Device Architecture (CUDA) on a graphic processing unit (GPU) show the significant advantages of using GPU for large matrices (with millions of elements) in comparison with the CPU implementation from the OpenCV library (Intel, Santa Clara, CA, USA).Vukašin Stanojević, Lev Kazakovtsev, Predrag S. Stanimirović, Natalya Rezova, Guzel Shkaberinawork_xza5krlk2ngyhc3hwxuiikbs2qTue, 27 Sep 2022 00:00:00 GMTA streamlined quantum algorithm for topological data analysis with exponentially fewer qubits
https://scholar.archive.org/work/bfpxeg4apvglzfhkomsu4xnphe
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyse and classify data in machine learning applications. We present an improved quantum algorithm for computing persistent Betti numbers, and provide an end-to-end complexity analysis. Our approach provides large polynomial time improvements, and an exponential space saving, over existing quantum algorithms. Subject to gap dependencies, our algorithm obtains an almost quintic speedup in the number of datapoints over rigorous state-of-the-art classical algorithms for calculating the persistent Betti numbers to constant additive error - the salient task for applications. However, this may be reduced to closer to quadratic when compared against heuristic classical methods and observed scalings. We discuss whether quantum algorithms can achieve an exponential speedup for tasks of practical interest, as claimed previously. We conclude that there is currently no evidence that this is the case.Sam McArdle, András Gilyén, Mario Bertawork_bfpxeg4apvglzfhkomsu4xnpheMon, 26 Sep 2022 00:00:00 GMTObstructions to faster diameter computation: Asteroidal sets
https://scholar.archive.org/work/t7krlf4h5fahlgfhe5ygabpy44
An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let Ext_α be the class of all connected graphs whose quotient graph obtained from modular decomposition contains no more than α pairwise nonadjacent extremities. Our main contributions are as follows. First, we prove that the diameter of every m-edge graph in Ext_α can be computed in deterministic O(α^3 m^3/2) time. We then improve the runtime to linear for all graphs with bounded clique-number. Furthermore, we can compute an additive +1-approximation of all vertex eccentricities in deterministic O(α^2 m) time. This is in sharp contrast with general m-edge graphs for which, under the Strong Exponential Time Hypothesis (SETH), one cannot compute the diameter in O(m^2-ϵ) time for any ϵ > 0. As important special cases of our main result, we derive an O(m^3/2)-time algorithm for exact diameter computation within dominating pair graphs of diameter at least six, and an O(k^3m^3/2)-time algorithm for this problem on graphs of asteroidal number at most k. We end up presenting an improved algorithm for chordal graphs of bounded asteroidal number, and a partial extension of our results to the larger class of all graphs with a dominating target of bounded cardinality. Our time upper bounds in the paper are shown to be essentially optimal under plausible complexity assumptions.Guillaume Ducoffework_t7krlf4h5fahlgfhe5ygabpy44Mon, 26 Sep 2022 00:00:00 GMTOptimization problems in graphs with locational uncertainty
https://scholar.archive.org/work/gswwrkoycrbexdtpahixxxpwrm
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances of the chosen set of edges for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are NP-hard even when the feasible sets consist either of all spanning trees or of all s-t paths. Given this hardness, we propose an exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose a conservative approximation and show its equivalence to the affine decision rule approximation in the context of Euclidean distances. We compare our algorithms to three deterministic reformulations on instances inspired by the scientific literature for the Steiner tree problem and a facility location problem.Marin Bougeret, Jérémy Omer, Michael Posswork_gswwrkoycrbexdtpahixxxpwrmMon, 26 Sep 2022 00:00:00 GMTThe Landscape of Distributed Complexities on Trees and Beyond
https://scholar.archive.org/work/pk3a3mrbwvdxvdh6ume35gs23m
We study the local complexity landscape of locally checkable labeling (LCL) problems on constant-degree graphs with a focus on complexities below log^* n. Our contribution is threefold: Our main contribution is that we complete the classification of the complexity landscape of LCL problems on trees in the LOCAL model, by proving that every LCL problem with local complexity o(log^* n) has actually complexity O(1). This result improves upon the previous speedup result from o(loglog^* n) to O(1) by [Chang, Pettie, FOCS 2017]. In the related LCA and Volume models [Alon, Rubinfeld, Vardi, Xie, SODA 2012, Rubinfeld, Tamir, Vardi, Xie, 2011, Rosenbaum, Suomela, PODC 2020], we prove the same speedup from o(log^* n) to O(1) for all bounded degree graphs. Similarly, we complete the classification of the LOCAL complexity landscape of oriented d-dimensional grids by proving that any LCL problem with local complexity o(log^* n) has actually complexity O(1). This improves upon the previous speed-up from o(√(log^* n)) by Suomela in [Chang, Pettie, FOCS 2017].Christoph Grunau, Vaclav Rozhon, Sebastian Brandtwork_pk3a3mrbwvdxvdh6ume35gs23mFri, 23 Sep 2022 00:00:00 GMTUndirected (1+ε)-Shortest Paths via Minor-Aggregates: Near-Optimal Deterministic Parallel Distributed Algorithms
https://scholar.archive.org/work/avgfthkhgzgltjmalqqxpw37rq
This paper presents near-optimal deterministic parallel and distributed algorithms for computing (1+ε)-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this and other shortest-path problems to Õ(1) Minor-Aggregations. A Minor-Aggregation computes an aggregate (e.g., max or sum) of node-values for every connected component of some subgraph. Our reduction immediately implies: Optimal deterministic parallel (PRAM) algorithms with Õ(1) depth and near-linear work. Universally-optimal deterministic distributed (CONGEST) algorithms, whenever deterministic Minor-Aggregate algorithms exist. For example, an optimal Õ(HopDiameter(G))-round deterministic CONGEST algorithm for excluded-minor networks. Several novel tools developed for the above results are interesting in their own right: A local iterative approach for reducing shortest path computations "up to distance D" to computing low-diameter decompositions "up to distance D/2". Compared to the recursive vertex-reduction approach of [Li20], our approach is simpler, suitable for distributed algorithms, and eliminates many derandomization barriers. A simple graph-based Õ(1)-competitive ℓ_1-oblivious routing based on low-diameter decompositions that can be evaluated in near-linear work. The previous such routing [ZGY+20] was n^o(1)-competitive and required n^o(1) more work. A deterministic algorithm to round any fractional single-source transshipment flow into an integral tree solution. The first distributed algorithms for computing Eulerian orientations.Václav Rozhoň and Christoph Grunau and Bernhard Haeupler and Goran Zuzic and Jason Liwork_avgfthkhgzgltjmalqqxpw37rqFri, 23 Sep 2022 00:00:00 GMTImproved Distributed Network Decomposition, Hitting Sets, and Spanners, via Derandomization
https://scholar.archive.org/work/lnohfvsjgbdirlx37d5cq6dbcu
This paper presents significantly improved deterministic algorithms for some of the key problems in the area of distributed graph algorithms, including network decomposition, hitting sets, and spanners. As the main ingredient in these results, we develop novel randomized distributed algorithms that we can analyze using only pairwise independence, and we can thus derandomize efficiently. As our most prominent end-result, we obtain a deterministic construction for O(log n)-color O(log n ·logloglog n)-strong diameter network decomposition in Õ(log^3 n) rounds. This is the first construction that achieves almost log n in both parameters, and it improves on a recent line of exciting progress on deterministic distributed network decompositions [Rozhoň, Ghaffari STOC'20; Ghaffari, Grunau, Rozhoň SODA'21; Chang, Ghaffari PODC'21; Elkin, Haeupler, Rozhoň, Grunau FOCS'22].Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, Saeed Ilchi, Václav Rozhoňwork_lnohfvsjgbdirlx37d5cq6dbcuFri, 23 Sep 2022 00:00:00 GMTComputing solution space properties of combinatorial optimization problems via generic tensor networks
https://scholar.archive.org/work/xee5elvwfjdvlmht37lzrjqc7m
We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the independent set problem as an example, we show how all these solution space properties can be computed in the unified approach of generic tensor networks. We demonstrate the versatility of this computational tool by applying it to several examples, including computing the entropy constant for hardcore lattice gases, studying the overlap gap properties, and analyzing the performance of quantum and classical algorithms for finding maximum independent sets.Jin-Guo Liu, Xun Gao, Madelyn Cain, Mikhail D. Lukin, Sheng-Tao Wangwork_xee5elvwfjdvlmht37lzrjqc7mFri, 23 Sep 2022 00:00:00 GMTCombinatorial optimization and reasoning with graph neural networks
https://scholar.archive.org/work/dszclpgdgfgzrnd562tfbceni4
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by enhancing exact solvers. The inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at optimization and machine learning researchers.Quentin Cappart, Didier Chételat, Elias Khalil, Andrea Lodi, Christopher Morris, Petar Veličkovićwork_dszclpgdgfgzrnd562tfbceni4Fri, 23 Sep 2022 00:00:00 GMT