Pub Date : 2024-11-08DOI: 10.1016/j.ic.2024.105235
Xian Wu, Lvzhou Li
Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound for the synthesis of n-wire reversible circuits was proved. Whether this lower bound has a matching upper bound was listed as one of the future challenging open problems in the survey (Saeedi and Markov (2013) [1]). In this paper we propose an algorithm to implement an arbitrary n-wire reversible circuit with no more than elementary gates, and thus close the open problem.
人们对可逆电路进行了广泛而深入的研究，在数字信号处理、密码学，特别是量子计算等各个领域都有大量应用。2003 年，人们证明了 n 线可逆电路合成的下界 Ω(2nn/logn)。这一下界是否有匹配的上界被列为调查报告中未来具有挑战性的开放问题之一（Saeedi 和 Markov (2013) [1]）。在本文中，我们提出了一种用不超过 O(2nn/logn) 的基本门实现任意 n 线可逆电路的算法，从而解决了这个开放问题。
{"title":"Asymptotically optimal synthesis of reversible circuits","authors":"Xian Wu, Lvzhou Li","doi":"10.1016/j.ic.2024.105235","DOIUrl":"10.1016/j.ic.2024.105235","url":null,"abstract":"<div><div>Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>/</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> for the synthesis of <em>n</em>-wire reversible circuits was proved. Whether this lower bound has a matching upper bound was listed as one of the future challenging open problems in the survey (Saeedi and Markov (2013) <span><span>[1]</span></span>). In this paper we propose an algorithm to implement an arbitrary <em>n</em>-wire reversible circuit with no more than <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>/</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> elementary gates, and thus close the open problem.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105235"},"PeriodicalIF":0.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-04DOI: 10.1016/j.ic.2024.105234
Danielle Marshall , Dominic Orchard
Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, strict linearity is limiting since there exist useful communication patterns that rely on non-linear behaviours. For example, shared channels can repeatedly spawn a process with binary communication along a fresh linear channel. Non-linearity can be introduced in a controlled way through the concept of graded modal types, which are a framework encompassing various kinds of coeffect (describing how computations make demands on their context). This paper shows how graded modalities can work alongside session types, enabling various non-linear concurrency behaviours to be re-introduced precisely. The ideas are demonstrated using Granule, a functional language with linear, indexed, and graded modal types. We define a core calculus capturing the requisite features and our new graded primitives, then present an operational model and establish various key properties.
{"title":"Non-linear communication via graded modal session types","authors":"Danielle Marshall , Dominic Orchard","doi":"10.1016/j.ic.2024.105234","DOIUrl":"10.1016/j.ic.2024.105234","url":null,"abstract":"<div><div>Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, strict linearity is limiting since there exist useful communication patterns that rely on non-linear behaviours. For example, shared channels can repeatedly spawn a process with binary communication along a fresh linear channel. Non-linearity can be introduced in a controlled way through the concept of <em>graded modal types</em>, which are a framework encompassing various kinds of <em>coeffect</em> (describing how computations make demands on their context). This paper shows how graded modalities can work alongside session types, enabling various non-linear concurrency behaviours to be re-introduced precisely. The ideas are demonstrated using Granule, a functional language with linear, indexed, and graded modal types. We define a core calculus capturing the requisite features and our new graded primitives, then present an operational model and establish various key properties.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105234"},"PeriodicalIF":0.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 10.1016/j.ic.2024.105233
Paolo Baldan , Barbara König , Tommaso Padoan
Systems of fixpoint equations over complete lattices, which combine least and greatest fixpoints, often arise from verification tasks such as model checking and behavioural equivalence checking. In this paper we develop a theory of approximation in the style of abstract interpretation, where a system over some concrete domain is abstracted into a system on a suitable abstract domain, ensuring sound and possibly complete over-approximations of the solutions. We also show how up-to techniques, commonly used to simplify coinductive proofs, fit into this framework, interpreted as abstractions. Additionally, we characterise the solution of fixpoint equation systems through parity games, extending prior work limited to continuous lattices. This game-based approach allows for local algorithms that verify system properties, such as determining whether a state satisfies a formula or two states are behaviourally equivalent. We describe a local algorithm, that can be combined with abstraction and up-to techniques to speed up the computation.
{"title":"Systems of fixpoint equations: Abstraction, games, up-to techniques and local algorithms","authors":"Paolo Baldan , Barbara König , Tommaso Padoan","doi":"10.1016/j.ic.2024.105233","DOIUrl":"10.1016/j.ic.2024.105233","url":null,"abstract":"<div><div>Systems of fixpoint equations over complete lattices, which combine least and greatest fixpoints, often arise from verification tasks such as model checking and behavioural equivalence checking. In this paper we develop a theory of approximation in the style of abstract interpretation, where a system over some concrete domain is abstracted into a system on a suitable abstract domain, ensuring sound and possibly complete over-approximations of the solutions. We also show how up-to techniques, commonly used to simplify coinductive proofs, fit into this framework, interpreted as abstractions. Additionally, we characterise the solution of fixpoint equation systems through parity games, extending prior work limited to continuous lattices. This game-based approach allows for local algorithms that verify system properties, such as determining whether a state satisfies a formula or two states are behaviourally equivalent. We describe a local algorithm, that can be combined with abstraction and up-to techniques to speed up the computation.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105233"},"PeriodicalIF":0.8,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-21DOI: 10.1016/j.ic.2024.105232
Thomas Seiller , Luc Pellissier , Ulysse Léchine
We present a new abstract method for proving lower bounds in computational complexity based on the notion of topological and measurable entropy for dynamical systems. It is shown to generalise several previous lower bounds results from the literature in algebraic complexity, thus providing a unifying framework for “topological” proofs of lower bounds. We further use this method to prove that maxflow, a complete problem, is not computable in polylogarithmic time on parallel random access machines (prams) working with real numbers. This improves on a result of Mulmuley since the class of machines considered extends the class “prams without bit operations”, making more precise the relationship between Mulmuley's result and similar lower bounds on real prams.
{"title":"Unifying lower bounds for algebraic machines, semantically","authors":"Thomas Seiller , Luc Pellissier , Ulysse Léchine","doi":"10.1016/j.ic.2024.105232","DOIUrl":"10.1016/j.ic.2024.105232","url":null,"abstract":"<div><div>We present a new abstract method for proving lower bounds in computational complexity based on the notion of topological and measurable entropy for dynamical systems. It is shown to generalise several previous lower bounds results from the literature in algebraic complexity, thus providing a unifying framework for “topological” proofs of lower bounds. We further use this method to prove that <span>maxflow</span>, a <figure><img></figure> complete problem, is not computable in polylogarithmic time on parallel random access machines (<span>pram</span>s) working with real numbers. This improves on a result of Mulmuley since the class of machines considered extends the class “<span>pram</span>s without bit operations”, making more precise the relationship between Mulmuley's result and similar lower bounds on real <span>pram</span>s.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105232"},"PeriodicalIF":0.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 10.1016/j.ic.2024.105231
Bogdan Aman
In membrane systems evolution rules are constructed using only objects from a finite alphabet. In this paper we investigate rules in which variables are used. Namely, we define Variable P systems in which the rules containing variables need to be instantiated at the start of each computational step with values from some predefined sets of sets of objects.
The modelling power of variable P systems is described by simulating some basic arithmetic operations over a (multi)set of positive numbers (addition, multiplication, or a combination of them). The main advantage of using variable P systems consists in the small number of used rules regardless how many numbers are involved in the operation: e.g., the addition requires only 3 rules, while the multiplication only 27 rules.
在膜系统中，进化规则仅使用有限字母表中的对象来构建。本文将研究使用变量的规则。也就是说，我们定义了可变 P 系统，在该系统中，包含变量的规则需要在每个计算步骤开始时用一些预定义的对象集中的值实例化。可变 P 系统的建模能力通过模拟正数（多）集的一些基本算术运算（加法、乘法或它们的组合）来描述。使用变量 P 系统的主要优势在于，无论运算涉及多少个数字，所使用的规则数量都很少：例如，加法运算只需 3 条规则，而乘法运算只需 27 条规则。
{"title":"Introducing variables in the evolution rules of P systems","authors":"Bogdan Aman","doi":"10.1016/j.ic.2024.105231","DOIUrl":"10.1016/j.ic.2024.105231","url":null,"abstract":"<div><div>In membrane systems evolution rules are constructed using only objects from a finite alphabet. In this paper we investigate rules in which variables are used. Namely, we define Variable P systems in which the rules containing variables need to be instantiated at the start of each computational step with values from some predefined sets of sets of objects.</div><div>The modelling power of variable P systems is described by simulating some basic arithmetic operations over a (multi)set of positive numbers (addition, multiplication, or a combination of them). The main advantage of using variable P systems consists in the small number of used rules regardless how many numbers are involved in the operation: e.g., the addition requires only 3 rules, while the multiplication only 27 rules.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105231"},"PeriodicalIF":0.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.ic.2024.105230
Yaqiao Li , Pierre McKenzie
A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and studied. Some new or simpler proofs of known bounds are uncovered. Branching program resources and the new measures are compared extensively. The new variants are developed in part in the hope of tackling read-k branching programs for the tree evaluation problem. Other computation problems are studied as well. In particular, a common view of a function studied by Gál and a function studied by Bollig and Wegener leads to the general combinatorics of blocking sets. Technical combinatorial results of independent interest are obtained. New leads towards further progress are discussed. An exponential lower bound for non-deterministic read-k branching programs for the GEN function is also derived, independently from the new measures.
只读分支程序是一个已知合理下限但仍不完整的计算模型。这里定义并研究了在研究一次读取分支程序中成功的复杂性度量的变体。此外，还揭示了已知边界的一些新的或更简单的证明。对分支程序资源和新度量方法进行了广泛比较。新变体的开发部分是希望解决树评估问题中的读k分支程序。我们还研究了其他计算问题。特别是，对加尔所研究的函数以及博利格和韦格纳所研究的函数的共同看法，引出了阻塞集的一般组合学。我们还获得了具有独立意义的技术组合结果。讨论了取得进一步进展的新线索。此外，还得出了 GEN 函数的非确定读 k 分支程序的指数下限，这与新措施无关。
{"title":"Perspective on complexity measures targeting read-once branching programs","authors":"Yaqiao Li , Pierre McKenzie","doi":"10.1016/j.ic.2024.105230","DOIUrl":"10.1016/j.ic.2024.105230","url":null,"abstract":"<div><div>A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and studied. Some new or simpler proofs of known bounds are uncovered. Branching program resources and the new measures are compared extensively. The new variants are developed in part in the hope of tackling read-<em>k</em> branching programs for the tree evaluation problem. Other computation problems are studied as well. In particular, a common view of a function studied by Gál and a function studied by Bollig and Wegener leads to the general combinatorics of blocking sets. Technical combinatorial results of independent interest are obtained. New leads towards further progress are discussed. An exponential lower bound for non-deterministic read-<em>k</em> branching programs for the GEN function is also derived, independently from the new measures.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105230"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.ic.2024.105229
James C.A. Main , Mickael Randour
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis.
Optimal strategies may require randomisation when dealing with inherently probabilistic goals, balancing multiple objectives, or in contexts of partial information. There is no unique way to define randomised strategies. For instance, one can use so-called mixed strategies or behavioural ones. In the most general setting, these two classes do not share the same expressiveness. A seminal result in game theory — Kuhn's theorem — asserts their equivalence in games of perfect recall.
This result crucially relies on the possibility for strategies to use infinite memory, i.e., unlimited knowledge of all past observations. However, computer systems are finite in practice. Hence it is pertinent to restrict our attention to finite-memory strategies, defined as automata with outputs. Randomisation can be implemented in these in different ways: the initialisation, outputs or transitions can be randomised or deterministic respectively. Depending on which aspects are randomised, the expressiveness of the corresponding class of finite-memory strategies differs.
In this work, we study two-player concurrent stochastic games and provide a complete taxonomy of the classes of finite-memory strategies obtained by varying which of the three aforementioned components are randomised. Our taxonomy holds in games of perfect and imperfect information with perfect recall, and in games with more than two players. We also provide an adapted taxonomy for games with imperfect recall.
{"title":"Different strokes in randomised strategies: Revisiting Kuhn's theorem under finite-memory assumptions","authors":"James C.A. Main , Mickael Randour","doi":"10.1016/j.ic.2024.105229","DOIUrl":"10.1016/j.ic.2024.105229","url":null,"abstract":"<div><div>Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis.</div><div>Optimal strategies may require randomisation when dealing with inherently probabilistic goals, balancing multiple objectives, or in contexts of partial information. There is no unique way to define randomised strategies. For instance, one can use so-called <em>mixed</em> strategies or <em>behavioural</em> ones. In the most general setting, these two classes do not share the same expressiveness. A seminal result in game theory — <em>Kuhn's theorem</em> — asserts their equivalence in games of perfect recall.</div><div>This result crucially relies on the possibility for strategies to use <em>infinite memory</em>, i.e., unlimited knowledge of all past observations. However, computer systems are finite in practice. Hence it is pertinent to restrict our attention to <em>finite-memory</em> strategies, defined as automata with outputs. Randomisation can be implemented in these in different ways: the <em>initialisation</em>, <em>outputs</em> or <em>transitions</em> can be randomised or deterministic respectively. Depending on which aspects are randomised, the expressiveness of the corresponding class of finite-memory strategies differs.</div><div>In this work, we study two-player concurrent stochastic games and provide a complete taxonomy of the classes of finite-memory strategies obtained by varying which of the three aforementioned components are randomised. Our taxonomy holds in games of perfect and imperfect information with perfect recall, and in games with more than two players. We also provide an adapted taxonomy for games with imperfect recall.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105229"},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.ic.2024.105228
Beatrice Amico, Carlo Combi, Romeo Rizzi, Pietro Sala
In this paper, we propose a methodology for deriving a new kind of approximate temporal functional dependencies, called Approximate Predictive Functional Dependencies (APFDs), based on a three-window framework and on a multi-temporal relational model. Different features are proposed for the Observation Window (OW), where we observe predictive data, for the Waiting Window (WW), and for the Prediction Window (PW), where the predicted event occurs. We then consider the concept of approximation for such APFDs, introduce new error measures, and discuss different strategies for deriving APFDs. We discuss the quality, i.e., the informative content, of the derived AFDs by considering their entropy and information gain. Moreover, we outline the results in deriving APFDs focusing on the Acute Kidney Injury (AKI). We use real clinical data contained in the MIMIC III dataset related to patients from Intensive Care Units to show the applicability of our approach to real-world data.
{"title":"Predictive mining of multi-temporal relations","authors":"Beatrice Amico, Carlo Combi, Romeo Rizzi, Pietro Sala","doi":"10.1016/j.ic.2024.105228","DOIUrl":"10.1016/j.ic.2024.105228","url":null,"abstract":"<div><div>In this paper, we propose a methodology for deriving a new kind of approximate temporal functional dependencies, called Approximate Predictive Functional Dependencies (APFDs), based on a three-window framework and on a multi-temporal relational model. Different features are proposed for the Observation Window (OW), where we observe predictive data, for the Waiting Window (WW), and for the Prediction Window (PW), where the predicted event occurs. We then consider the concept of approximation for such APFDs, introduce new error measures, and discuss different strategies for deriving APFDs. We discuss the quality, i.e., the informative content, of the derived AFDs by considering their entropy and information gain. Moreover, we outline the results in deriving APFDs focusing on the Acute Kidney Injury (AKI). We use real clinical data contained in the MIMIC III dataset related to patients from Intensive Care Units to show the applicability of our approach to real-world data.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105228"},"PeriodicalIF":0.8,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142422711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-27DOI: 10.1016/j.ic.2024.105227
Yung-Chung Chiu, Hsueh-I Lu
For vertices u and v of an n-vertex graph G, a uv-trail of G is an induced uv-path of G that is not a shortest uv-path of G. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known polynomial-time algorithm, running in time, to either output a uv-trail of G or ensure that G admits no uv-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of Boolean matrices, leading to a largely improved -time algorithm. Our result improves the previous -time algorithm by Cook, Horsfield, Preissmann, Robin, Seymour, Sintiari, Trotignon, and Vušković [Journal of Combinatorial Theory, Series B, 2024] for recognizing graphs with all holes the same length, and reduces the running time to .
对于 n 个顶点图 G 的顶点 u 和 v，G 的 uv 轨迹是 G 的诱导 uv 路径，它不是 G 的最短 uv 路径。Berger、Seymour 和 Spirkl [Discrete Mathematics 2021]给出了以前已知的唯一多项式时间算法，运行时间为 O(n18)，可以输出 G 的 uv 轨迹或确保 G 不允许 uv 轨迹。我们将复杂度降低到执行 n2×n2 布尔矩阵多对数乘法所需的时间，从而大大改进了 O(n4.75)-time 算法。我们的结果改进了库克、霍斯菲尔德、普雷斯曼、罗宾、西摩、辛蒂亚里、特罗蒂尼翁和武什科维奇[《组合理论学报》，B 辑，2024 年]先前的 O(n21)-time 算法，用于识别所有孔长度相同的图，并将运行时间减少到 O(n7.75)。
{"title":"Blazing a trail via matrix multiplications: A faster algorithm for non-shortest induced paths","authors":"Yung-Chung Chiu, Hsueh-I Lu","doi":"10.1016/j.ic.2024.105227","DOIUrl":"10.1016/j.ic.2024.105227","url":null,"abstract":"<div><div>For vertices <em>u</em> and <em>v</em> of an <em>n</em>-vertex graph <em>G</em>, a <em>uv-trail</em> of <em>G</em> is an induced <em>uv</em>-path of <em>G</em> that is not a shortest <em>uv</em>-path of <em>G</em>. Berger, Seymour, and Spirkl [<em>Discrete Mathematics</em> 2021] gave the previously only known polynomial-time algorithm, running in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>18</mn></mrow></msup><mo>)</mo></math></span> time, to either output a <em>uv</em>-trail of <em>G</em> or ensure that <em>G</em> admits no <em>uv</em>-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> Boolean matrices, leading to a largely improved <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4.75</mn></mrow></msup><mo>)</mo></math></span>-time algorithm. Our result improves the previous <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>21</mn></mrow></msup><mo>)</mo></math></span>-time algorithm by Cook, Horsfield, Preissmann, Robin, Seymour, Sintiari, Trotignon, and Vušković [<em>Journal of Combinatorial Theory, Series B</em>, 2024] for recognizing graphs with all holes the same length, and reduces the running time to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>7.75</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105227"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1016/j.ic.2024.105225
Yuan Qiu , Jinyan Liu , Di Wang
This paper explores estimating Generalized Linear Models (GLMs) when agents are strategic and privacy-conscious. We aim to design mechanisms that encourage truthful reporting, protect privacy, and ensure outputs are close to the true parameters. Initially, we address models with sub-Gaussian covariates and heavy-tailed responses with finite fourth moments, proposing a novel private, closed-form estimator. Our mechanism features: (1) -joint differential privacy with high probability; (2) -approximate Bayes Nash equilibrium for -fraction of agents; (3) error in parameter estimation; (4) individual rationality for of agents; (5) payment budget. We then extend our approach to linear regression with heavy-tailed data, using an -norm shrinkage operator to propose a similar estimator and payment scheme.
{"title":"Truthful and privacy-preserving generalized linear models","authors":"Yuan Qiu , Jinyan Liu , Di Wang","doi":"10.1016/j.ic.2024.105225","DOIUrl":"10.1016/j.ic.2024.105225","url":null,"abstract":"<div><p>This paper explores estimating Generalized Linear Models (GLMs) when agents are strategic and privacy-conscious. We aim to design mechanisms that encourage truthful reporting, protect privacy, and ensure outputs are close to the true parameters. Initially, we address models with sub-Gaussian covariates and heavy-tailed responses with finite fourth moments, proposing a novel private, closed-form estimator. Our mechanism features: (1) <span><math><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>-joint differential privacy with high probability; (2) <span><math><mi>o</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></math></span>-approximate Bayes Nash equilibrium for <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span>-fraction of agents; (3) <span><math><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> error in parameter estimation; (4) individual rationality for <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span> of agents; (5) <span><math><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> payment budget. We then extend our approach to linear regression with heavy-tailed data, using an <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-norm shrinkage operator to propose a similar estimator and payment scheme.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105225"},"PeriodicalIF":0.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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