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Cops and Robbers on Dynamic Graphs: Offline and Online Case 动态图表上的警察和劫匪:离线和在线案例
4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2023-03-16 DOI: 10.46298/dmtcs.8784
Stefan Balev, Juan Jiménez Laredo, Ioannis Lamprou, Yoann Pigné, Eric Sanlaville
{"title":"Cops and Robbers on Dynamic Graphs: Offline and Online Case","authors":"Stefan Balev, Juan Jiménez Laredo, Ioannis Lamprou, Yoann Pigné, Eric Sanlaville","doi":"10.46298/dmtcs.8784","DOIUrl":"https://doi.org/10.46298/dmtcs.8784","url":null,"abstract":"We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the underlying graph of the model. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n 2k+1 T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs, i.e., with at most linear number of edges. We prove λ + 1 cops suffice to capture the robber in any underlying graph with n − 1 + λ edges. Further, we define a family of underlying graphs with n−1+λ edges where λ−1 cops are necessary (and sufficient) for capture.","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135488558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On intervals of the consecutive pattern poset 关于连续模式偏序集的区间
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/DMTCS.6380
S. Elizalde, Peter R. W. McNamara
{"title":"On intervals of the consecutive pattern poset","authors":"S. Elizalde, Peter R. W. McNamara","doi":"10.46298/DMTCS.6380","DOIUrl":"https://doi.org/10.46298/DMTCS.6380","url":null,"abstract":"International audience\u0000 \u0000 The consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives. In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and we characterize disconnected and shellable intervals. We also show that most intervals are not shellable and have Mo ̈bius function equal to zero.\u0000","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41452698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Noncrossing partitions, toggles, and homomesy 非交叉分区、切换和同构
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/dmtcs.6378
David M. Einstein, Miriam Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp, Simon Rubinstein-Salzedo
{"title":"Noncrossing partitions, toggles, and homomesy","authors":"David M. Einstein, Miriam Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp, Simon Rubinstein-Salzedo","doi":"10.46298/dmtcs.6378","DOIUrl":"https://doi.org/10.46298/dmtcs.6378","url":null,"abstract":"International audience\u0000 \u0000 We introduce n(n − 1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions. We show that for many operations T of this kind, a surprisingly large family of functions f on S (including the function that sends π to the number of blocks of π) exhibits the homomesy phenomenon: the average of f over the elements of a T -orbit is the same for all T -orbits. Our methods apply more broadly to toggle operations on independent sets of certain graphs.\u0000","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44791793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Brick polytopes, lattices and Hopf algebras 砖形多面体、格和Hopf代数
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/dmtcs.6401
Vincent Pilaud
{"title":"Brick polytopes, lattices and Hopf algebras","authors":"Vincent Pilaud","doi":"10.46298/dmtcs.6401","DOIUrl":"https://doi.org/10.46298/dmtcs.6401","url":null,"abstract":"International audience\u0000 \u0000 Generalizing the connection between the classes of the sylvester congruence and the binary trees, we show that the classes of the congruence of the weak order on Sn defined as the transitive closure of the rewriting rule UacV1b1 ···VkbkW ≡k UcaV1b1 ···VkbkW, for letters a < b1,...,bk < c and words U,V1,...,Vk,W on [n], are in bijection with acyclic k-triangulations of the (n + 2k)-gon, or equivalently with acyclic pipe dreams for the permutation (1,...,k,n + k,...,k + 1,n + k + 1,...,n + 2k). It enables us to transport the known lattice and Hopf algebra structures from the congruence classes of ≡k to these acyclic pipe dreams, and to describe the product and coproduct of this algebra in terms of pipe dreams. Moreover, it shows that the fan obtained by coarsening the Coxeter fan according to the classes of ≡k is the normal fan of the corresponding brick polytope\u0000","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43942195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relaxations of the matroid axioms I: Independence, Exchange and Circuits 拟阵公理的松弛Ⅰ：独立性、交换性和电路
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/dmtcs.6365
J. A. Samper
{"title":"Relaxations of the matroid axioms I: Independence, Exchange and Circuits","authors":"J. A. Samper","doi":"10.46298/dmtcs.6365","DOIUrl":"https://doi.org/10.46298/dmtcs.6365","url":null,"abstract":"International audience\u0000 \u0000 Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axioms needed to prove them. We illustrate this by discussing Tutte polynomials. Furthermore, we extend a conjecture of Stanley on h-vectors and provide evidence to show that the extension is better suited than matroids to study the conjecture.\u0000","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46550289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
DHD-puzzles DHD谜题
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/dmtcs.6332
Sabine Beil
{"title":"DHD-puzzles","authors":"Sabine Beil","doi":"10.46298/dmtcs.6332","DOIUrl":"https://doi.org/10.46298/dmtcs.6332","url":null,"abstract":"International audience\u0000 \u0000 In this work triangular puzzles that are composed of unit triangles with labelled edges are considered. To be more precise, the labelled unit triangles that we allow are on the one hand the puzzle pieces that compute Schubert calculus and on the other hand the flipped K-theory puzzle piece. The motivation for studying such puzzles comes from the fact that they correspond to a class of oriented triangular fully packed loop configurations. The main result that is presented is an expression for the number of these puzzles with a fixed boundary in terms of Littlewood- Richardson coefficients.","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49329822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A dual approach to structure constants for K-theory of Grassmannians 求解格拉斯曼k理论结构常数的对偶方法
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/DMTCS.6361
Huilan Li, J. Morse, Patrick Shields
{"title":"A dual approach to structure constants for K-theory of Grassmannians","authors":"Huilan Li, J. Morse, Patrick Shields","doi":"10.46298/DMTCS.6361","DOIUrl":"https://doi.org/10.46298/DMTCS.6361","url":null,"abstract":"International audience\u0000 \u0000 The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants of the Grothendieck ring of a Grassmannian variety with respect to itsbasis of Schubert structure sheaves in a similar way; we address the problem of expanding the generating functions forskew reverse-plane partitions into the basis of polynomials which are Hall-dual to stable Grothendieck polynomials. From this point of view, we produce a chain of bijections leading to Buch’s K-theoretic Littlewood-Richardson rule.\u0000","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45121547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A noncommutative geometric LR rule 一个非交换几何LR规则
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/dmtcs.6367
Stephanie van Willigenburg, V. Tewari, Edward Richmond
{"title":"A noncommutative geometric LR rule","authors":"Stephanie van Willigenburg, V. Tewari, Edward Richmond","doi":"10.46298/dmtcs.6367","DOIUrl":"https://doi.org/10.46298/dmtcs.6367","url":null,"abstract":"The geometric Littlewood-Richardson (LR) rule is a combinatorial algorithm for computing LR coefficients derived from degenerating the Richardson variety into a union of Schubert varieties in the Grassmannian. Such rules were first given by Vakil and later generalized by Coskun. In this paper we give a noncommutative version of the geometric LR rule. As a consequence, we establish a geometric explanation for the positivity of noncommutative LR coefficients in certain cases.","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47711743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Quasi-isomorphisms of cluster algebras and the combinatorics of webs (extended abstract) 簇代数的拟同构与网的组合(扩展抽象)
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2020-04-22 DOI: 10.46298/DMTCS.6395
C. Fraser
{"title":"Quasi-isomorphisms of cluster algebras and the combinatorics of webs (extended abstract)","authors":"C. Fraser","doi":"10.46298/DMTCS.6395","DOIUrl":"https://doi.org/10.46298/DMTCS.6395","url":null,"abstract":"International audience\u0000 \u0000 We provide bijections between the cluster variables (and clusters) in two families of cluster algebras which have received considerable attention. These cluster algebras are the ones associated with certain Grassmannians of k-planes, and those associated with certain spaces of decorated SLk-local systems in the disk in the work of Fock and Goncharov. When k is 3, this bijection can be described explicitly using the combinatorics of Kuperberg's basis of non-elliptic webs. Using our bijection and symmetries of these cluster algebras, we provide evidence for conjectures of Fomin and Pylyavskyy concerning cluster variables in Grassmannians of 3-planes. We also prove their conjecture that there are infinitely many indecomposable nonarborizable webs in the Grassmannian of 3-planes in 9-dimensional space.\u0000","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41929051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
DGR: Deep Gender Recognition of Human Speech 人类语言的深度性别识别
IF 0.7 4区 数学
Discrete Mathematics and Theoretical Computer Science Pub Date : 2019-03-04 DOI: 10.20944/PREPRINTS201903.0047.V1
Rami Suleiman Alkhawaldeh
{"title":"DGR: Deep Gender Recognition of Human Speech","authors":"Rami Suleiman Alkhawaldeh","doi":"10.20944/PREPRINTS201903.0047.V1","DOIUrl":"https://doi.org/10.20944/PREPRINTS201903.0047.V1","url":null,"abstract":"The speech entailed in human voice comprises essentially para-linguistic information used in many voice-recognition applications. Gender voice-recognition is considered one of the pivotal parts to be detected from a given voice, a task that involves certain complications. In order to distinguish gender from a voice signal, a set of techniques have been employed to determine relevant features to be utilized for building a model from a training set. This model is useful for determining the gender (i.e, male or female) from a voice signal. The contributions are involved in two folds: (i) providing analysis information about well-known voice signal features using a prominent dataset, (ii) studying various machine learning models of different theoretical families to classify the voice gender, and (iii) using three prominent feature selection algorithms to find promisingly optimal features for improving classification models. Experimental results show the importance of sub-features over others, which are vital for enhancing the efficiency of classification models performance. Experimentation reveals that the best recall value is equal to 99.97%; 99.7% of two models of Deep Learning (DL) and Support Vector Machine (SVM) and with feature selection the best recall value is 100% for SVM techniques.","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47522373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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