Embedded Systems and Applications最新文献_第10页

Improved Search of Relevant Points for Nearest-Neighbor Classification 改进的最近邻分类相关点搜索

Embedded Systems and Applications Pub Date : 2022-03-07 DOI: 10.48550/arXiv.2203.03567

Alejandro Flores-Velazco

引用次数: 1

Online Spanners in Metric Spaces 度量空间中的在线扳手

Embedded Systems and Applications Pub Date : 2022-02-21 DOI: 10.4230/LIPIcs.ESA.2022.18

S. Bhore, Arnold Filtser, Hadi Khodabandeh, Csaba D. T'oth

{"title":"Online Spanners in Metric Spaces","authors":"S. Bhore, Arnold Filtser, Hadi Khodabandeh, Csaba D. T'oth","doi":"10.4230/LIPIcs.ESA.2022.18","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2022.18","url":null,"abstract":"Given a metric space $mathcal{M}=(X,delta)$, a weighted graph $G$ over $X$ is a metric $t$-spanner of $mathcal{M}$ if for every $u,v in X$, $delta(u,v)le d_G(u,v)le tcdot delta(u,v)$, where $d_G$ is the shortest path metric in $G$. In this paper, we construct spanners for finite sets in metric spaces in the online setting. Here, we are given a sequence of points $(s_1, ldots, s_n)$, where the points are presented one at a time (i.e., after $i$ steps, we saw $S_i = {s_1, ldots , s_i}$). The algorithm is allowed to add edges to the spanner when a new point arrives, however, it is not allowed to remove any edge from the spanner. The goal is to maintain a $t$-spanner $G_i$ for $S_i$ for all $i$, while minimizing the number of edges, and their total weight. We construct online $(1+varepsilon)$-spanners in Euclidean $d$-space, $(2k-1)(1+varepsilon)$-spanners for general metrics, and $(2+varepsilon)$-spanners for ultrametrics. Most notably, in Euclidean plane, we construct a $(1+varepsilon)$-spanner with competitive ratio $O(varepsilon^{-3/2}logvarepsilon^{-1}log n)$, bypassing the classic lower bound $Omega(varepsilon^{-2})$ for lightness, which compares the weight of the spanner, to that of the MST.","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114640397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

SAT Backdoors: Depth Beats Size SAT后门:深度胜过尺寸

Embedded Systems and Applications Pub Date : 2022-02-16 DOI: 10.4230/LIPIcs.ESA.2022.46

Jannik Dreier, S. Ordyniak, Stefan Szeider

{"title":"SAT Backdoors: Depth Beats Size","authors":"Jannik Dreier, S. Ordyniak, Stefan Szeider","doi":"10.4230/LIPIcs.ESA.2022.46","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2022.46","url":null,"abstract":"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, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by M\"{a}hlmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. Bounded backdoor size implies bounded backdoor depth, but there are formulas of constant backdoor depth and arbitrarily large backdoor size. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes. We base our FPT approximation algorithm on a sophisticated notion of obstructions, extending M\"{a}hlmann et al.'s obstruction trees in various ways, including the addition of separator obstructions. We develop the algorithm through a new game-theoretic framework that simplifies the reasoning about backdoors. Finally, we show that bounded backdoor depth captures tractable classes of CNF formulas not captured by any known method.","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121862177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Hedonic Games and Treewidth Revisited 重新审视Hedonic Games和Treewidth

Embedded Systems and Applications Pub Date : 2022-02-14 DOI: 10.4230/LIPIcs.ESA.2022.64

T. Hanaka, M. Lampis

{"title":"Hedonic Games and Treewidth Revisited","authors":"T. Hanaka, M. Lampis","doi":"10.4230/LIPIcs.ESA.2022.64","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2022.64","url":null,"abstract":"We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an edge-weighted digraph $G=(V,E)$, and the weight of an arc $uv$ denotes the utility $u$ gains by being in the same coalition as $v$. We focus on (arguably) the most basic stability question about such a game: given a graph, does a Nash stable solution exist and can we find it efficiently? We study the (parameterized) complexity of ASHG stability when the underlying graph has treewidth $t$ and maximum degree $Delta$. The current best FPT algorithm for this case was claimed by Peters [AAAI 2016], with time complexity roughly $2^{O(Delta^5t)}$. We present an algorithm with parameter dependence $(Delta t)^{O(Delta t)}$, significantly improving upon the parameter dependence on $Delta$ given by Peters, albeit with a slightly worse dependence on $t$. Our main result is that this slight performance deterioration with respect to $t$ is actually completely justified: we observe that the previously claimed algorithm is incorrect, and that in fact no algorithm can achieve dependence $t^{o(t)}$ for bounded-degree graphs, unless the ETH fails. This, together with corresponding bounds we provide on the dependence on $Delta$ and the joint parameter establishes that our algorithm is essentially optimal for both parameters, under the ETH. We then revisit the parameterization by treewidth alone and resolve a question also posed by Peters by showing that Nash Stability remains strongly NP-hard on stars under additive preferences. Nevertheless, we also discover an island of mild tractability: we show that Connected Nash Stability is solvable in pseudo-polynomial time for constant $t$, though with an XP dependence on $t$ which, as we establish, cannot be avoided.","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126671793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Insertion Time of Random Walk Cuckoo Hashing below the Peeling Threshold 低于剥离阈值的随机游走布谷鸟哈希插入时间

Embedded Systems and Applications Pub Date : 2022-02-11 DOI: 10.4230/LIPIcs.ESA.2022.87

Stefan Walzer

引用次数: 4

Approximation Algorithms for ROUND-UFP and ROUND-SAP round - up和ROUND-SAP的近似算法

Embedded Systems and Applications Pub Date : 2022-02-07 DOI: 10.4230/LIPIcs.ESA.2022.71

Debajyoti Kar, Arindam Khan, Andreas Wiese

{"title":"Approximation Algorithms for ROUND-UFP and ROUND-SAP","authors":"Debajyoti Kar, Arindam Khan, Andreas Wiese","doi":"10.4230/LIPIcs.ESA.2022.71","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2022.71","url":null,"abstract":"We study ROUND-UFP and ROUND-SAP, two generalizations of the classical BIN PACKING problem that correspond to the unsplittable flow problem on a path (UFP) and the storage allocation problem (SAP), respectively. We are given a path with capacities on its edges and a set of tasks where for each task we are given a demand and a subpath. In ROUND-UFP, the goal is to find a packing of all tasks into a minimum number of copies (rounds) of the given path such that for each copy, the total demand of tasks on any edge does not exceed the capacity of the respective edge. In ROUND-SAP, the tasks are considered to be rectangles and the goal is to find a non-overlapping packing of these rectangles into a minimum number of rounds such that all rectangles lie completely below the capacity profile of the edges. We show that in contrast to BIN PACKING, both the problems do not admit an asymptotic polynomial-time approximation scheme (APTAS), even when all edge capacities are equal. However, for this setting, we obtain asymptotic $(2+varepsilon)$-approximations for both problems. For the general case, we obtain an $O(loglog n)$-approximation algorithm and an $O(loglogfrac{1}{delta})$-approximation under $(1+delta)$-resource augmentation for both problems. For the intermediate setting of the no bottleneck assumption (i.e., the maximum task demand is at most the minimum edge capacity), we obtain absolute $12$- and asymptotic $(16+varepsilon)$-approximation algorithms for ROUND-UFP and ROUND-SAP, respectively.","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116149918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Improved Prophet Inequalities for Combinatorial Welfare Maximization with (Approximately) Subadditive Agents (近似)次加性主体组合福利最大化的改进先知不等式

Embedded Systems and Applications Pub Date : 2022-02-01 DOI: 10.4230/LIPIcs.ESA.2020.82

Hanrui Zhang

引用次数: 5

Counting Simplices in Hypergraph Streams 超图流中的简单计数

Embedded Systems and Applications Pub Date : 2021-12-21 DOI: 10.4230/LIPIcs.ESA.2022.32

Amit Chakrabarti, Themistoklis K. Haris

{"title":"Counting Simplices in Hypergraph Streams","authors":"Amit Chakrabarti, Themistoklis K. Haris","doi":"10.4230/LIPIcs.ESA.2022.32","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2022.32","url":null,"abstract":"We consider the problem of space-efficiently estimating the number of simplices in a hypergraph stream. This is the most natural hypergraph generalization of the highly-studied problem of estimating the number of triangles in a graph stream. Our input is a k -uniform hypergraph H with n vertices and m hyperedges, each hyperedge being a k -sized subset of vertices. A k -simplex in H is a subhypergraph on k + 1 vertices X such that all k + 1 possible hyperedges among X exist in H . The goal is to process the hyperedges of H , which arrive in an arbitrary order as a data stream, and compute a good estimate of T k ( H ), the number of k -simplices in H . We design a suite of algorithms for this problem. As with triangle-counting in graphs (which is the special case k = 2), sublinear space is achievable but only under a promise of the form T k ( H ) ≥ T . Under such a promise, our algorithms use at most four passes and together imply a space bound of O for each fixed k ≥ 3, in order to guarantee an estimate within (1 ± ε ) T k ( H ) with probability ≥ 1 − δ . We also give a simpler 1-pass algorithm that achieves O (cid:16) ε − 2 log δ − 1 log n · ( m/T ) (cid:16) ∆ E + ∆ − 1 /k V (cid:17)(cid:17) space, where ∆ E (respectively, ∆ V ) denotes the maximum number of k -simplices that share a hyperedge (respectively, a vertex), which generalizes a previous result for the k = 2 case. We complement these algorithmic results with space lower bounds of the form Ω( ε − 2 ), Ω( m 1+1 /k /T ), Ω( m/T 1 − 1 /k ) and Ω( m ∆ 1 /kV /T ) for multi-pass algorithms and Ω( m ∆ E /T ) for 1-pass algorithms, which show that some of the dependencies on parameters in our upper bounds are nearly tight. Our techniques extend and generalize several different ideas previously developed for triangle counting in graphs, using appropriate innovations to handle the more complicated combinatorics of hypergraphs. 2012 ACM Subject Classification Theory of computation → Sketching and sampling","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"78 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128092957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Conditional Lower Bounds for Dynamic Geometric Measure Problems 动态几何测量问题的条件下界

Embedded Systems and Applications Pub Date : 2021-12-19 DOI: 10.4230/LIPIcs.ESA.2022.39

Justin Dallant, J. Iacono

{"title":"Conditional Lower Bounds for Dynamic Geometric Measure Problems","authors":"Justin Dallant, J. Iacono","doi":"10.4230/LIPIcs.ESA.2022.39","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2022.39","url":null,"abstract":"We give new polynomial lower bounds for a number of dynamic measure problems in computational geometry. These lower bounds hold in the Word-RAM model, conditioned on the hardness of either 3SUM, APSP, or the Online Matrix-Vector Multiplication problem [Henzinger et al., STOC 2015]. In particular we get lower bounds in the incremental and fully-dynamic settings for counting maximal or extremal points in R 3 , diﬀerent variants of Klee’s Measure Problem, problems related to ﬁnding the largest empty disk in a set of points, and querying the size of the i ’th convex layer in a planar set of points. We also answer a question of Chan et al. [SODA 2022] by giving a conditional lower bound for dynamic approximate square set cover. While many conditional lower bounds for dynamic data structures have been proven since the seminal work of Pătraşcu [STOC 2010], few of them relate to computational geometry problems. This is the ﬁrst paper focusing on this topic. Most problems we consider can be solved in O ( n log n ) time in the static case and their dynamic versions have only been approached from the perspective of improving known upper bounds. One exception to this is Klee’s measure problem in R 2 , for which Chan [CGTA 2010] gave an unconditional Ω( √ n ) lower bound on the worst-case update time. By a similar approach, we show that such a lower bound also holds for an important special case of Klee’s measure problem in R 3 known as the Hypervolume Indicator problem, even for amortized runtime in the incremental setting. discussions about the topic of this paper.","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127009738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Localized Geometric Moves to Compute Hyperbolic Structures on Triangulated 3-Manifolds 三角化3流形上计算双曲结构的局部几何移动

Embedded Systems and Applications Pub Date : 2021-12-13 DOI: 10.4230/LIPIcs.ESA.2022.78

Clément Maria, Owen Rouill'e

引用次数: 0