Foundations of Software Technology and Theoretical Computer Science最新文献_第2页

Black Box Absolute Reconstruction for Sums of Powers of Linear Forms 线性形式的幂和的黑箱绝对重构

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-10-11 DOI: 10.4230/LIPIcs.FSTTCS.2022.24

P. Koiran, Subhayan Saha

{"title":"Black Box Absolute Reconstruction for Sums of Powers of Linear Forms","authors":"P. Koiran, Subhayan Saha","doi":"10.4230/LIPIcs.FSTTCS.2022.24","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.24","url":null,"abstract":"We study the decomposition of multivariate polynomials as sums of powers of linear forms. We give a randomized algorithm for the following problem: If a homogeneous polynomial $f in K[x_1 , . . . , x_n]$ (where $K subseteq mathbb{C}$) of degree $d$ is given as a blackbox, decide whether it can be written as a linear combination of $d$-th powers of linearly independent complex linear forms. The main novel features of the algorithm are: (1) For $d = 3$, we improve by a factor of $n$ on the running time from an algorithm by Koiran and Skomra. The price to be paid for this improvement though is that the algorithm now has two-sided error. (2) For $d>3$, we provide the first randomized blackbox algorithm for this problem that runs in time polynomial in $n$ and $d$ (in an algebraic model where only arithmetic operations and equality tests are allowed). Previous algorithms for this problem as well as most of the existing reconstruction algorithms for other classes appeal to a polynomial factorization subroutine. This requires extraction of complex polynomial roots at unit cost and in standard models such as the unit-cost RAM or the Turing machine this approach does not yield polynomial time algorithms. (3) For $d>3$, when $f$ has rational coefficients, the running time of the blackbox algorithm is polynomial in $n,d$ and the maximal bit size of any coefficient of $f$. This yields the first algorithm for this problem over $mathbb{C}$ with polynomial running time in the bit model of computation.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123423024","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

Concrete Categorical Model of a Quantum Circuit Description Language with Measurement 带有测量的量子电路描述语言的具体范畴模型

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-10-06 DOI: 10.4230/LIPIcs.FSTTCS.2021.51

Dongho Lee, Valentin Perrelle, B. Valiron, Zhaowei Xu

引用次数: 6

On Fair and Efficient Allocations of Indivisible Public Goods 论不可分割公共物品的公平有效分配

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-07-21 DOI: 10.4230/LIPIcs.FSTTCS.2021.22

J. Garg, Pooja Kulkarni, Aniket Murhekar

{"title":"On Fair and Efficient Allocations of Indivisible Public Goods","authors":"J. Garg, Pooja Kulkarni, Aniket Murhekar","doi":"10.4230/LIPIcs.FSTTCS.2021.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.22","url":null,"abstract":"We study fair allocation of indivisible public goods subject to cardinality (budget) constraints. In this model, we have n agents and m available public goods, and we want to select k ≤ m goods in a fair and efficient manner. We first establish fundamental connections between the models of private goods, public goods, and public decision making by presenting polynomial-time reductions for the popular solution concepts of maximum Nash welfare (MNW) and leximin. These mechanisms are known to provide remarkable fairness and efficiency guarantees in private goods and public decision making settings. We show that they retain these desirable properties even in the public goods case. We prove that MNW allocations provide fairness guarantees of Proportionality up to one good (Prop1), 1/n approximation to Round Robin Share (RRS), and the efficiency guarantee of Pareto Optimality (PO). Further, we show that the problems of finding MNW or leximin-optimal allocations are NP-hard, even in the case of constantly many agents, or binary valuations. This is in sharp contrast to the private goods setting that admits polynomial-time algorithms under binary valuations. We also design pseudo-polynomial time algorithms for computing an exact MNW or leximin-optimal allocation for the cases of (i) constantly many agents, and (ii) constantly many goods with additive valuations. We also present an O(n)-factor approximation algorithm for MNW which also satisfies RRS, Prop1, and 1/2-Prop. 2012 ACM Subject Classification Theory of computation → Mathematical optimization","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115065681","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: 8

Approximate Trace Reconstruction via Median String (in Average-Case) 通过中值字符串近似重建轨迹(在平均情况下)

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-07-20 DOI: 10.4230/LIPIcs.FSTTCS.2021.11

Diptarka Chakraborty, Debarati Das, Robert Krauthgamer

引用次数: 4

From local to global determinacy in concurrent graph games 从局部确定性到全局确定性

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-07-08 DOI: 10.4230/LIPIcs.FSTTCS.2021.41

Benjamin Bordais, P. Bouyer, Stéphane Le Roux

{"title":"From local to global determinacy in concurrent graph games","authors":"Benjamin Bordais, P. Bouyer, Stéphane Le Roux","doi":"10.4230/LIPIcs.FSTTCS.2021.41","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.41","url":null,"abstract":"In general, finite concurrent two-player reachability games are only determined in a weak sense: the supremum probability to win can be approached via stochastic strategies, but cannot be realized. We introduce a class of concurrent games that are determined in a much stronger sense, and in a way, it is the larger class with this property. To this end, we introduce the notion of emph{local interaction} at a state of a graph game: it is a emph{game form} whose outcomes (i.e. a table whose entries) are the next states, which depend on the concurrent actions of the players. By definition, a game form is emph{determined} iff it always yields games that are determined via deterministic strategies when used as a local interaction in a Nature-free, one-shot reachability game. We show that if all the local interactions of a graph game with Borel objective are determined game forms, the game itself is determined: if Nature does not play, one player has a winning strategy; if Nature plays, both players have deterministic strategies that maximize the probability to win. This constitutes a clear-cut separation: either a game form behaves poorly already when used alone with basic objectives, or it behaves well even when used together with other well-behaved game forms and complex objectives. Existing results for positional and finite-memory determinacy in turn-based games are extended this way to concurrent games with determined local interactions (CG-DLI).","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122446707","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

The Degree of a Finite Set of Words 有限词集的度

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-06-28 DOI: 10.4230/LIPIcs.FSTTCS.2020.54

D. Perrin, Andrew Ryzhikov

引用次数: 1

Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing 几何遇上向量:多维填充的近似算法

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-06-26 DOI: 10.4230/LIPIcs.FSTTCS.2022.23

Arindam Khan, Eklavya Sharma, K. V. N. Sreenivas

{"title":"Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing","authors":"Arindam Khan, Eklavya Sharma, K. V. N. Sreenivas","doi":"10.4230/LIPIcs.FSTTCS.2022.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.23","url":null,"abstract":"We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{textrm{th}}$ item has width $w(i)$, height $h(i)$, and $d$ nonnegative weights $v_1(i), v_2(i), ldots, v_{d}(i)$. Our goal is to get an axis-parallel non-overlapping packing of the items into square bins so that for all $j in [d]$, the sum of the $j^{textrm{th}}$ weight of items in each bin is at most 1. This is a natural problem arising in logistics, resource allocation, and scheduling. Despite being well studied in practice, surprisingly, approximation algorithms for this problem have rarely been explored. We first obtain two simple algorithms for GVBP having asymptotic approximation ratios $6(d+1)$ and $3(1 + ln(d+1) + varepsilon)$. We then extend the Round-and-Approx (R&A) framework [Bansal-Khan, SODA'14] to wider classes of algorithms, and show how it can be adapted to GVBP. Using more sophisticated techniques, we obtain better approximation algorithms for GVBP, and we get further improvement by combining them with the R&A framework. This gives us an asymptotic approximation ratio of $2(1+ln((d+4)/2))+varepsilon$ for GVBP, which improves to $2.919+varepsilon$ for the special case of $d=1$. We obtain further improvement when the items are allowed to be rotated. We also present algorithms for a generalization of GVBP where the items are high dimensional cuboids.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122562633","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

Near-Optimal Cayley Expanders for Abelian Groups 阿贝尔群的近最优Cayley展开器

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-05-03 DOI: 10.4230/LIPIcs.FSTTCS.2021.24

Akhil Jalan, Dana Moshkovitz

引用次数: 5

Reachability and Matching in Single Crossing Minor Free Graphs 单交次自由图的可达性与匹配

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-03-25 DOI: 10.4230/LIPIcs.FSTTCS.2021.16

Samir Datta, Chetan Gupta, Rahul Jain, A. Mukherjee, V. Sharma, Raghunath Tewari

引用次数: 2

Hard QBFs for Merge Resolution 合并解析的硬QBFs

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2020-12-12 DOI: 10.4230/LIPIcs.FSTTCS.2020.12

Olaf Beyersdorff, Joshua Blinkhorn, M. Mahajan, Tomáš Peitl, Gaurav Sood

引用次数: 4