Acta Informatica最新文献_第8页

Exploration of k-edge-deficient temporal graphs 缺k边时间图的探索

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-08-27 DOI: 10.1007/s00236-022-00421-5

Thomas Erlebach, Jakob T. Spooner

{"title":"Exploration of k-edge-deficient temporal graphs","authors":"Thomas Erlebach, Jakob T. Spooner","doi":"10.1007/s00236-022-00421-5","DOIUrl":"10.1007/s00236-022-00421-5","url":null,"abstract":"<div>A temporal graph with lifetime L is a sequence of L graphs (G_1, ldots ,G_L), called layers, all of which have the same vertex set V but can have different edge sets. The underlying graph is the graph with vertex set V that contains all the edges that appear in at least one layer. The temporal graph is always connected if each layer is a connected graph, and it is k-edge-deficient if each layer contains all except at most k edges of the underlying graph. For a given start vertex s, a temporal exploration is a temporal walk that starts at s, traverses at most one edge in each layer, and visits all vertices of the temporal graph. We show that always-connected, k-edge-deficient temporal graphs with sufficient lifetime can always be explored in (O(kn log n)) time steps. We also construct always-connected, k-edge-deficient temporal graphs for which any exploration requires (varOmega (n log k)) time steps. For always-connected, 1-edge-deficient temporal graphs, we show that O(n) time steps suffice for temporal exploration.</div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"59 4","pages":"387 - 407"},"PeriodicalIF":0.6,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-022-00421-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42775206","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}

引用次数: 2

Properties of graphs specified by a regular language 由常规语言指定的图的属性

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-08-12 DOI: 10.1007/s00236-022-00427-z

Volker Diekert, Henning Fernau, Petra Wolf

{"title":"Properties of graphs specified by a regular language","authors":"Volker Diekert, Henning Fernau, Petra Wolf","doi":"10.1007/s00236-022-00427-z","DOIUrl":"10.1007/s00236-022-00427-z","url":null,"abstract":"<div>Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property (varPhi ). What happens if this question is modified in a way that we get a possibly infinite family of graphs as an input, and the question is if there is a graph satisfying (varPhi ) in the family? We approach this question by using formal languages for specifying families of graphs, in particular by regular sets of words. We show that certain graph properties can be decided by studying the syntactic monoid of the specification language L if a certain torsion condition is satisfied. This condition holds trivially if L is regular. More specifically, we use a natural binary encoding of finite graphs over a binary alphabet (varSigma ), and we define a regular set (mathbb {G}subseteq varSigma ^*) such that every nonempty word (win mathbb {G}) defines a finite and nonempty graph. Also, graph properties can then be syntactically defined as languages over (varSigma ). Then, we ask whether the automaton (mathcal {A}) specifies some graph satisfying a certain property (varPhi ). Our structural results show that we can answer this question for all “typical” graph properties. In order to show our results, we split L into a finite union of subsets and every subset of this union defines in a natural way a single finite graph F where some edges and vertices are marked. The marked graph in turn defines an infinite graph (F^infty ) and therefore the family of finite subgraphs of (F^infty ) where F appears as an induced subgraph. This yields a geometric description of all graphs specified by L based on splitting L into finitely many pieces; then using the notion of graph retraction, we obtain an easily understandable description of the graphs in each piece.</div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"59 4","pages":"357 - 385"},"PeriodicalIF":0.6,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-022-00427-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41686213","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}

引用次数: 3

Preface to Klaus-Jörn Lange Festschrift 克劳斯-约恩-兰格艺术节序言

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-08-09 DOI: 10.1007/s00236-022-00426-0

Henning Fernau, Markus Holzer, Petra Wolf

引用次数: 0

On the decidability of finding a positive ILP-instance in a regular set of ILP-instances 关于在正则ILP实例集中找到正ILP实例的判定性

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-08-04 DOI: 10.1007/s00236-022-00429-x

Petra Wolf

{"title":"On the decidability of finding a positive ILP-instance in a regular set of ILP-instances","authors":"Petra Wolf","doi":"10.1007/s00236-022-00429-x","DOIUrl":"10.1007/s00236-022-00429-x","url":null,"abstract":"<div>The regular intersection emptiness problem for a decision problem P (({{textit{int}}_{{mathrm {Reg}}}})(P)) is to decide whether a potentially infinite regular set of encoded P-instances contains a positive one. Since ({{textit{int}}_{{mathrm {Reg}}}})(P) is decidable for some NP-complete problems and undecidable for others, its investigation provides insights in the nature of NP-complete problems. Moreover, the decidability of the ({{textit{int}}_{{mathrm {Reg}}}})-problem is usually achieved by exploiting the regularity of the set of instances; thus, it also establishes a connection to formal language and automata theory. We consider the ({{textit{int}}_{{mathrm {Reg}}}})-problem for the well-known NP-complete problem Integer Linear Programming (ILP). It is shown that any DFA that describes a set of ILP-instances (in a natural encoding) can be reduced to a finite core of instances that contains a positive one if and only if the original set of instances did. This result yields the decidability of ({{textit{int}}_{{mathrm {Reg}}}})(ILP).</div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"59 4","pages":"505 - 519"},"PeriodicalIF":0.6,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-022-00429-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41604344","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}

引用次数: 0

Pushdown automata and constant height: decidability and bounds 下推自动机与常高：可判定性与边界

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-07-27 DOI: 10.1007/s00236-022-00434-0

Giovanni Pighizzini, Luca Prigioniero

引用次数: 4

The regular languages of wire linear AC0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$^0$$end{document} wire linear AC0documentclass[12pt]｛minimal｝ usepackage｛amsmath｝ userpackage{wasysym｝usepackage{amsfonts｝ use package{amssymb｝ user package{asbssy｝use package{mathrsfs｝ usapackage{upgeek｝setlength｛doddsedmargin｝｛-69pt｝ begin｛document｝$^0$end

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-07-25 DOI: 10.1007/s00236-022-00432-2

M. Cadilhac, Charles Paperman

引用次数: 0

Reoptimization of parameterized problems 参数化问题的再优化

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-07-25 DOI: 10.1007/s00236-022-00428-y

Hans-Joachim Böckenhauer, Elisabet Burjons, Martin Raszyk, Peter Rossmanith

{"title":"Reoptimization of parameterized problems","authors":"Hans-Joachim Böckenhauer, Elisabet Burjons, Martin Raszyk, Peter Rossmanith","doi":"10.1007/s00236-022-00428-y","DOIUrl":"10.1007/s00236-022-00428-y","url":null,"abstract":"<div>Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to neighboring instances. We combine both techniques, in order to better classify the complexity of problems in the parameterized setting. Specifically, we see that some problems in the class of compositional problems, which do not have polynomial kernels under standard complexity-theoretic assumptions, do have polynomial kernels under the reoptimization model for some local modifications. We also observe that, for some other local modifications, these same problems do not have polynomial kernels unless (mathbf{NP}subseteq mathbf{coNP/poly}). We find examples of compositional problems, whose reoptimization versions do not have polynomial kernels under any of the considered local modifications. Finally, in another negative result, we prove that the reoptimization version of Connected Vertex Cover does not have a polynomial kernel unless Set Cover has a polynomial compression. In a different direction, looking at problems with polynomial kernels, we find that the reoptimization version of Vertex Cover has a polynomial kernel of size (varvec{2k+1}) using crown decompositions only, which improves the size of the kernel achievable with this technique in the classic problem.</div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"59 4","pages":"427 - 450"},"PeriodicalIF":0.6,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-022-00428-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40334166","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}

引用次数: 6

The regular languages of wire linear AC(^0) 有线线性AC（^0）的正则语言

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-07-25 DOI: 10.1007/s00236-022-00432-2

Michaël Cadilhac, Charles Paperman

引用次数: 0

Careful synchronization of partial deterministic finite automata 部分确定性有限自动机的谨慎同步

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-07-22 DOI: 10.1007/s00236-022-00433-1

Hanan Shabana, M. V. Volkov

引用次数: 1

Operational complexity and pumping lemmas 操作复杂性和泵浦引理

IF 0.6 4区计算机科学

Acta Informatica Pub Date : 2022-07-20 DOI: 10.1007/s00236-022-00431-3

Jürgen Dassow, Ismaël Jecker

{"title":"Operational complexity and pumping lemmas","authors":"Jürgen Dassow, Ismaël Jecker","doi":"10.1007/s00236-022-00431-3","DOIUrl":"10.1007/s00236-022-00431-3","url":null,"abstract":"<div>The well-known pumping lemma for regular languages states that, for any regular language L, there is a constant p (depending on L) such that the following holds: If (win L) and (vert wvert ge p), then there are words (xin V^{*}), (yin V^+), and (zin V^{*}) such that (w=xyz) and (xy^tzin L) for (tge 0). The minimal pumping constant ({{{,mathrm{mpc},}}(L)}) of L is the minimal number p for which the conditions of the pumping lemma are satisfied. We investigate the behaviour of ({{{,mathrm{mpc},}}}) with respect to operations, i. e., for an n-ary regularity preserving operation (circ ), we study the set ({g_{circ }^{{{,mathrm{mpc},}}}(k_1,k_2,ldots ,k_n)}) of all numbers k such that there are regular languages (L_1,L_2,ldots ,L_n) with ({{{,mathrm{mpc},}}(L_i)=k_i}) for (1le ile n) and ({{{,mathrm{mpc},}}(circ (L_1,L_2,ldots ,L_n)=~k}). With respect to Kleene closure, complement, reversal, prefix and suffix-closure, circular shift, union, intersection, set-subtraction, symmetric difference,and concatenation, we determine ({g_{circ }^{{{,mathrm{mpc},}}}(k_1,k_2,ldots ,k_n)}) completely. Furthermore, we give some results with respect to the minimal pumping length where, in addition, (vert xyvert le p) has to hold.</div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"59 4","pages":"337 - 355"},"PeriodicalIF":0.6,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-022-00431-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43609320","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}

引用次数: 1