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ACM SIGMOD International Conference on Management of Data (SIGMOD)

作者： Li, Zhaoheng Pi, Xinyu Wu, Mingyuan Univ Illinois Urbana IL 61801 USA

ISBN: (纸本)9781450383431

In settings such as corporate management where team structure is highly volatile and large-scale personnel changes are commonplace, the ability to simultaneously replace multiple team members in a team is highly appreciated. We define the problem of Subteam Replacement to address this observation: given a team of people embedded in a social network to complete a certain task, and a subset of members - subteam - in this team which has become unavailable, find another set of people which can perform the subteam's role in the larger team. We propose a holistic evaluation metric and scalable solution for Subteam Replacement with strong theoretical guarantees and perform quantitative evaluations on both generated and real datasets.

关键词： approximation algorithm team recommendation graph kernels graph mining

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On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphs

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ANNALES DE L INSTITUT HENRI POINCARE D 2021年第3期8卷 459-489页

作者： Bencs, Ferenc Davies, Ewan Patel, Viresh Regts, Guus HAS Alfred Renyi Inst Math Realtanoda Utca 13-15 H-1053 Budapest Hungary Cent European Univ Dept Math Kozep Europai Egyet Nador U 9 H-1051 Budapest Hungary Univ Amsterdam Korteweg de Vries Inst Math Sci Pk 105-107 NL-1098 XG Amsterdam Netherlands Univ Colorado Dept Comp Sci 1111 Engn DrECOT 717430 UCB Boulder CO 80309 USA

For a graph G = (V, E), k is an element of N, and complex numbers w = (w(e))(e)(is an element of E) the partition function of the multivariate Potts model is defined as Z(G;k, w) : = Sigma(phi:V ->[k]) Pi(e=uv is an element of E phi(u)=phi(v)) w(e), where [k] := (1, ..., k}. In this paper we give zero-free regions for the partition function of the anti-ferromagnetic Potts model on bounded degree graphs. In particular we show that for any Delta is an element of N and any k >= e Delta + 1, there exists an open set U in the complex plane that contains the interval [0, 1) such that Z(G;k, w) not equal 0 for any graph G = (V, E) of maximum degree at most Delta and any w is an element of U-E. (Here e denotes the base of the natural logarithm.) For small values of Delta we are able to give better results. As an application of our results we obtain improved bounds on k for the existence of deterministic approximation algorithms for counting the number of proper k-colourings of graphs of small maximum degree.

关键词： Anti-ferromagnetic Potts model counting proper colourings partition function approximation algorithm complex zeros

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Partitioning Into Prescribed Number of Cycles and Mod k T-join With Slack 11

Partitioning Into Prescribed Number of Cycles and Mod <i>k</...

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11th Latin and American algorithms, Graphs and Optimization Symposium (LAGOS)

作者： Barrett, Jordan Bendayan, Salomon Li, Yanjia Reed, Bruce McGill Univ Dept Math Montreal PQ Canada Univ Waterloo Dept Combinator & Optimizat Waterloo ON Canada McGill Univ Dept Comp Sci Montreal PQ Canada

The input to a PPNC instance is integers n and p, and a non-negative real weighting of the edges of the clique K-n on the vertex set {1,..., n}We are asked to find a set of p disjoint cycles spanning {1,..., n} and subject to this such that the sum of the weights of the edges is minimized We provide an efficient approximation algorithm for the metric version of this problem which has an approximation ratio of 4 if p <= n/5 sand an approximation ratio of 51 for larger p. For p > n/5, our algorithm uses a subroutine which approximately solves the Mod 3 T-join With Slack problem. The input to an instance of Mod k T-join with Slack consists of integers n and B, a non-negative weighting of the edges of the clique K-n, and a label 1(v) from {0,1, ... k - 1} on each vertex of K-n. We are asked to find the minimum weight spanning forest F from amongst those satisfying Sigma(T is an element of F)((Sigma(v is an element of(T)) 1(v)) mod k) <= B. If k = 2 and B = 0 this is the well-studied T-join problem which can be solved exactly in polynomial time. (C) 2021 The Authors. Published by Elsevier B.V.

关键词： Hamiltonian p-median problem T-join approximation algorithm Graph partition

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Improved approximation algorithm for the jump number of interval orders

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Electronic Notes in Discrete Mathematics 2013年 40卷 193-198页

作者： Krysztowiak, Przemysław Faculty of Mathematics and Computer Science Nicolaus Copernicus University Toruń Poland

The jump number problem for posets is to find a linear extension in which the number of incomparable adjacent pairs is minimized. In this paper the class of interval orders is considered. Three 3/2-approximation algorithms for this problem have been known for some time. By a previous work of Mitas, the problem may be reformulated as a subgraph packing task. We prove that the problem reduces also to a set cover task, and we establish an improved bound of 1.484 to the approximation ratio of the jump number on interval orders. © 2013 Elsevier B.V.

关键词： approximation algorithm Combinatorial optimization Interval order Jump number Linear extension Poset Scheduling Set cover Subgraph packing

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A VECTORIZATION SCHEME FOR NONCONVEX SET OPTIMIZATION PROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 2022年第2期32卷 1184-1209页

作者： Eichfelder, Gabriele Quintana, Ernest Rocktaschel, Stefan Tech Univ Ilmenau Inst Math Po 10 05 65 D-98684 Ilmenau Germany

In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution sets approximate, in a specific sense, that of the set-valued problem with arbitrary accuracy. We also examine particular classes of set-valued mappings for which the corresponding set optimization problem is equivalent to a multiobjective optimization problem in the generated family. Surprisingly, this includes set-valued mappings with a convex graph.

关键词： set optimization set approach nonconvex sets approximation algorithm multi-objective optimization

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Channel modeling of wireless 3D-chip based on ray-tracing

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MICROELECTRONICS JOURNAL 2022年 119卷

作者： Ren, Chao Hou, Jingze Pan, Biao Univ Sci & Technol Beijing Sch Comp & Commun Engn & Shunde Grad Sch Beijing Peoples R China Univ Sci & Technol Beijing Beijing Peoples R China Beihang Univ Sch Integrated Circuit Sci & Engn MIIT Key Lab Spintron Beijing Peoples R China

The resource constraints and accuracy requirements for Internet of Things (IoT) memory chips need threedimensional (3D) monolithic integrated circuits, of which the increasing stack layers (currently more than 176) also cause excessive energy consumption and increasing wire length. In this paper, we propose and describe the channel modeling for wireless 3D chips based on ray-tracing. However, due to the reflection and refraction characteristics in each layer, the complex and diverse wireless paths in 3D chips add great difficulty to the channel characterization. To facilitate the modeling in massive layer wireless 3D chips based on ray-tracing, both boundary-less and boundary-constrained wireless 3D chips models are proposed based on ray-tracing, of which the channel gain can be obtained by a computational efficient approximate algorithm. These wireless 3D models with approximation algorithm can well characterize the wireless 3D chip channel in aspect of complete reflection and refraction characteristics, and avoid massive wired connections, high power consumption of cross-layer communication and high-complexity of 3D chips channel characterization. Numerical results show that: (1) The difference rate between the two models is lower than 0.001% (signal transmit through 20 layers);(2) the channel gain decreases sharply if refract time increases;and (3) the approximate algorithm can achieve an acceptable accuracy (error rate lower than 0.1%).

关键词： Ray-tracing Channel gain Three-dimensional chip approximation algorithm

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A New approximation algorithm for Vertex Cover Problem

A New Approximation Algorithm for Vertex Cover Problem

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IEEE International Conference on Machine Intelligence Research and Advancement (ICMIRA)

作者： Dahiya, Sonika Guru Gobind Singh Indraprastha Univ USICT Dept CSE IT Delhi 110078 India

ISBN: (纸本)9780769550138

Vertex Cover Problem is one among NP-Complete problems. So neither the proof of existence of a optimal solution algorithm nor the proof of no existence of such solution has been given yet. So it is desirable to try to find a near optimal solution. In this paper we give a brief introduction of existing algorithms and propose a new heuristic algorithm. This new algorithm has polynomial running time and produces a near optimal solution for the unweighted graphs and outperforms compared to the existing approximation algorithms for graph.

关键词： approximation algorithm approximation ratio degree pendant edge pendant vertex vertex cover vertex cover problem

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Near-Optimal NP-Hardness of Approximating MAX k-CSPR

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THEORY OF COMPUTING 2022年 18卷 1-29页

作者： Manurangsi, Pasin Nakkiran, Preetum Trevisan, Luca Univ Calif Berkeley Berkeley CA USA Google Res Mountain View CA 94043 USA Univ Calif San Diego Halicioglu Data Sci Inst La Jolla CA 92093 USA Bocconi Univ Dept Decis Sci Comp Sci Milan Italy

We prove almost optimal hardness for MAX k-CSPR. In MAX k-CSPR, we are given a set of constraints, each of which depends on at most k variables. Each variable can take any value from 1, 2,. .., R. The goal is to find an assignment to variables that maximizes the number of satisfied constraints. We show that, for any k >= 2 and R >= 16, it is NP-hard to approximate MAX k- CSPR to within factor k(O(k))(logR)(k/2) =Rk-1. In the regime where 3 <= k = o(logR= log logR), this ratio improves upon Chan's O(k/Rk-2) factor NP-hardness of approximation of MAX k-CSPR (J. ACM 2016). Moreover, when k = 2, our result matches the best known hardness result of Khot, Kindler, Mossel and O'Donnell (SIAM J. Comp. 2007). We remark here that NPhardness of an approximation factor of 2(O(k)) log(kR)/Rk-1 is implicit in the (independent) work of Khot and Saket (ICALP 2015), which is better than our ratio for all k >= 3. In addition to the above hardness result, by extending an algorithm for MAX 2- CSPR by Kindler, Kolla and Trevisan (SODA 2016), we provide an Omega(logR/Rk-1)-approximation algorithm for MAX k-CSPR. Thanks to Khot and Saket's result, this algorithm is tight up to a factor of O(k(2)) when k <= R-O(1). In comparison, when 3 <= k is a constant, the previously best known algorithm achieves an O(k/Rk-1)-approximation for the problem, which is a factor of O(k logR) from the inapproximability ratio in contrast to our gap of O(k(2)).

关键词： constraint satisfaction hardness of approximation approximation algorithm

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Fair and Representative Subset Selection from Data Streams 21

Fair and Representative Subset Selection from Data Streams

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30th World Wide Web Conference (WWW)

作者： Wang, Yanhao Fabbri, Francesco Mathioudakis, Michael Univ Helsinki Helsinki Finland Pompeu Fabra Univ Barcelona Spain Eurecat Barcelona Spain

ISBN: (纸本)9781450383127

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be formulated as maximizing a monotone submodular function subject to a cardinality constraint k. In this work, we consider the setting where data items in the stream belong to one of several disjoint groups and investigate the optimization problem with an additional fairness constraint that limits selection to a given number of items from each group. We then propose efficient algorithms for the fairness-aware variant of the streaming submodular maximization problem. In particular, we first give a (1/2 - epsilon)-approximation algorithm that requires O(1/epsilon log k/epsilon) passes over the stream for any constant epsilon > 0. Moreover, we give a single-pass streaming algorithm that has the same approximation ratio of (1/2 - epsilon) when unlimited buffer sizes and post-processing time are permitted, and discuss how to adapt it to more practical settings where the buffer sizes are bounded. Finally, we demonstrate the efficiency and effectiveness of our proposed algorithms on two real-world applications, namely maximum coverage on large graphs and personalized recommendation.

关键词： algorithmic fairness approximation algorithm data summarization streaming algorithm submodular maximization

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Simple approximation algorithms for Balanced MAX 2SAT

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algorithmICA 2018年第3期80卷 995-1012页

作者： Paul, Alice Poloczek, Matthias Williamson, David P. Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14850 USA

We study simple algorithms for the balanced MAX 2SAT problem, where we are given weighted clauses of length one and two with the property that for each variable x the total weight of clauses that x appears in equals the total weight of clauses for . We show that such instances have a simple structural property in that any optimal solution can satisfy at most the total weight of the clauses minus half the total weight of the unit clauses. Using this property and a novel analysis of the computation tree, we are able to show that a large class of greedy algorithms, including Johnson's algorithm, gives a -approximation algorithm for balanced MAX 2SAT;a similar statement is false for general MAX 2SAT instances. We further give a spectral 0.81-approximation algorithm for balanced MAX E2SAT instances (in which each clause has exactly 2 literals) by a reduction to a spectral algorithm of Trevisan for the maximum colored cut problem. We provide experimental results showing that this spectral algorithm performs well and is slightly better than Johnson's algorithm and the Goemans-Williamson semidefinite programming algorithm on balanced MAX E2SAT instances.

关键词： Maximum satisfiability approximation algorithm Greedy algorithm Spectral algorithm Balanced instances Priority algorithm

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