Acta Informatica最新文献

{"title":"Effects on distance energy of some special complete multipartite graphs by embedding an edge","authors":"Masood Ur Rehman,&nbsp;Muhammad Ajmal","doi":"10.1007/s00236-025-00491-1","DOIUrl":"10.1007/s00236-025-00491-1","url":null,"abstract":"<div><p>The distance energy of a simple undirected graph <span>(mathcal {G})</span>, denoted by <span>(mathcal {E}_D(mathcal {G}))</span>, is the sum of the absolute values of the eigenvalues of the distance matrix <span>(D(mathcal {G}))</span> of <span>(mathcal {G})</span>. In this paper, we study the effects on distance energy of some special complete <i>t</i>-partite graphs due to embedding an edge. This paper is motivated by the study in a 2022 paper by Wang and Meng.\u0000</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144108446","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}

{"title":"Row-column combination of Dyck words","authors":"Stefano Crespi Reghizzi,&nbsp;Antonio Restivo,&nbsp;Pierluigi San Pietro","doi":"10.1007/s00236-025-00489-9","DOIUrl":"10.1007/s00236-025-00489-9","url":null,"abstract":"<div><p>We extend the notion of the Dyck language from words to two-dimensional arrays of symbols, i.e., pictures, using the row-column combination (also known as the crossword) of two Dyck languages over the same alphabet. In a Dyck crossword picture, each column and each row must be a word from the respective Dyck language. The pairing of open and closed parentheses in a Dyck word can be represented by edges connecting corresponding cells in the same row or column. This defines a <i>matching graph</i>, which serves as the two-dimensional analogue of the syntactic tree of a Dyck word. A matching graph is partitioned into simple circuits of unbounded length (always a multiple of four), whose labels form a regular language. These circuits exhibit a wide variety of forms and labelings, which we illustrate and partially classify. With a two-letter alphabet, a Dyck crossword is necessarily empty. The minimal non-trivial case, requiring an alphabet of size four, already generates all possible forms of matching graphs and is the primary focus of our study. We prove that the only picture with a single matching circuit (i.e., a Hamiltonian cycle) has size 2 by 2. Two key properties of Dyck words–cancellation and well-nesting–can be generalized to two dimensions, leading to two alternative definitions of 2D Dyck languages: <i>neutralizable </i> and <i>well-nested</i>. These languages are special cases of Dyck crossword pictures called quaternate, where all circuits have length 4 (i.e., are rectangles). This results in a strict language inclusion hierarchy: well-nested <span>(subset )</span> neutralizable <span>(subset )</span> quaternate <span>(subset )</span> Dyck crosswords. When the alphabet size exceeds four, not all combinations of row and column Dyck languages yield non-empty crosswords. To identify productive combinations, we introduce an <i>alphabetic graph</i>, where nodes represent alphabet symbols and edges represent their couplings. A matching circuit corresponds to the unrolling of an alphabetic graph circuit. Finally, we prove that Dyck crosswords are not tiling-recognizable, as expected for a definition extending Dyck word languages to pictures.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-025-00489-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117700","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}

{"title":"Deterministic real-time tree-walking-storage automata","authors":"Martin Kutrib,&nbsp;Uwe Meyer","doi":"10.1007/s00236-025-00488-w","DOIUrl":"10.1007/s00236-025-00488-w","url":null,"abstract":"<div><p>We study deterministic tree-walking-storage automata, which are finite-state devices equipped with a tree-like storage. These automata are generalized stack automata, where the linear stack storage is replaced by a non-linear tree-like stack. Therefore, tree-walking-storage automata have the ability to explore the interior of the tree storage without altering the contents, with the possible moves of the tree pointer corresponding to those of tree-walking automata. In addition, a tree-walking-storage automaton can append (push) non-existent descendants to a tree node and remove (pop) leaves from the tree. Here we are particularly considering the capacities of deterministic tree-walking-storage automata working in real time. It is shown that even the non-erasing variant can accept rather complicated unary languages as, for example, the language of words whose lengths are powers of two, or the language of words whose lengths are double Fibonacci numbers. Comparing the computational capacities with automata from the classical automata hierarchy, we derive that the family of languages accepted by real-time deterministic (non-erasing) tree-walking-storage automata is located between the regular and the deterministic context-sensitive languages. Moreover, the families are incomparable with the families of context-free and growing context-sensitive languages. It turns out that the devices under consideration accept unary languages in non-erasing mode that cannot be accepted by any classical stack automaton, even in erasing mode and arbitrary time. Basic closure properties of the induced families of languages are shown. In particular, we consider Boolean operations and AFL operations. It turns out that the two families in question have the same properties and, in particular, share all but one of these closure properties with the important family of deterministic context-free languages. Then, we consider the computational capacity of the counterpart to counter- and stack-counter automata, where the set of stack symbols is a singleton. Finally, we explore several decidability problems and show, that even for devices with a single tree symbol, the problems are all non-semidecidable by reductions of non-semidecidable problems of Turing machines.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-025-00488-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900799","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}

{"title":"Three-word codes ({a, aba, u}) and ({a, ab, v}) having finite completions","authors":"Chunhua Cao,&nbsp;Lei Liao,&nbsp;Zhongmei Yan,&nbsp;Di Yang,&nbsp;Yuguang Yuan","doi":"10.1007/s00236-025-00487-x","DOIUrl":"10.1007/s00236-025-00487-x","url":null,"abstract":"<div><p>Does every three-word code have a finite completion? Up to now, this famous question in the theory of codes remains open. Motivated by this problem, we construct several types of three-word codes with the form <span>({a, aba, u})</span> and <span>({a, ab, v})</span> which have finite completions.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840353","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}

{"title":"Visualization of bipartite graphs in limited window size","authors":"Alon Efrat,&nbsp;William Evans,&nbsp;Kassian Köck,&nbsp;Stephen Kobourov,&nbsp;Jacob Miller","doi":"10.1007/s00236-025-00483-1","DOIUrl":"10.1007/s00236-025-00483-1","url":null,"abstract":"<div><p>Bipartite graphs are commonly used to visualize objects and their features. An object may possess several features and several objects may share a common feature. The standard visualization of bipartite graphs, with objects and features on two (say horizontal) parallel lines at integer coordinates and edges drawn as line segments, can often be difficult to work with. A common task in visualization of such graphs is to consider one object and all its features. This naturally defines a drawing window, defined as the smallest interval that contains the x-coordinates of the object and all its features. We show that if both objects and features can be reordered, minimizing the average window size is NP-hard. However, if the features are fixed, then we provide an efficient polynomial-time algorithm for arranging the objects, so as to minimize the average window size. Finally, we introduce a different way of visualizing the bipartite graph, by placing the nodes of the two parts on two concentric circles. For this setting we also show NP-hardness for the general case and a polynomial-time algorithm when the features are fixed.\u0000</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-025-00483-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761776","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}

{"title":"The thief orienteering problem on 2-terminal series–parallel graphs","authors":"Andrew Bloch-Hansen,&nbsp;Roberto Solis-Oba","doi":"10.1007/s00236-025-00486-y","DOIUrl":"10.1007/s00236-025-00486-y","url":null,"abstract":"<div><p>In the thief orienteering problem an agent called a <i>thief</i> carries a knapsack of capacity <i>W</i> and has a time limit <i>T</i> to collect a set of items of total weight at most <i>W</i> and maximum profit along a simple path in a weighted graph <span>(G = (V, E))</span> from a start vertex <i>s</i> to an end vertex <i>t</i>. There is a set <i>I</i> of items each with weight <span>(w_{i})</span> and profit <span>(p_{i})</span> that are distributed among <span>(V{setminus }{s,t})</span>. The time needed by the thief to travel an edge depends on the length of the edge and the weight of the items in the knapsack at the moment when the edge is traversed. There is a polynomial-time approximation scheme for a relaxed version of the thief orienteering problem on directed acyclic graphs that produces solutions that use time at most <span>(T(1 + epsilon ))</span> for any constant <span>(epsilon &gt; 0)</span>. We give a polynomial-time algorithm for transforming instances of the problem on 2-terminal series–parallel graphs into equivalent instances of the thief orienteering problem on directed acyclic graphs; therefore, yielding a polynomial-time approximation scheme for the relaxed version of the thief orienteering problem on this graph class.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688433","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}

{"title":"On star-k-PCGs: exploring class boundaries for small k values","authors":"Angelo Monti,&nbsp;Blerina Sinaimeri","doi":"10.1007/s00236-025-00485-z","DOIUrl":"10.1007/s00236-025-00485-z","url":null,"abstract":"<div><p>A graph <span>(G=(V,E))</span> is a star-<i>k</i>-pairwise compatibility graph (star-<i>k</i>-PCG) if there exists a weight function <span>(w: V rightarrow mathbb {R}^+)</span> and <i>k</i> mutually exclusive intervals <span>(I_1, I_2, ldots I_k)</span>, such that there is an edge <span>(uv in E)</span> if and only if <span>(w(u)+w(v) in bigcup _i I_i)</span>. These graphs are related to two important classes of graphs: pairwise compatibility graphs (PCGs) and multithreshold graphs. It is known that for any graph <i>G</i> there exists a <i>k</i> such that <i>G</i> is a star-<i>k</i>-PCG. Thus, for a given graph <i>G</i> it is interesting to know which is the minimum <i>k</i> such that <i>G</i> is a star-<i>k</i>-PCG. We define this minimum <i>k</i> as the <i>star number</i> of the graph, denoted by <span>(gamma (G))</span>. Here we investigate the star number of simple graph classes, such as graphs of small size, caterpillars, cycles and grids. Specifically, we determine the exact value of <span>(gamma (G))</span> for all the graphs with at most 7 vertices. By doing so we show that the smallest graphs with star number 2 are only 4 and have exactly 5 vertices; the smallest graphs with star number 3 are only 3 and have exactly 7 vertices. Next, we provide a construction showing that the star number of caterpillars is one. Moreover, we show that the star number of cycles and two-dimensional grid graphs is 2 and that the star number of 4-dimensional grids is at least 3. Finally, we conclude with numerous open problems.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-025-00485-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668207","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}

{"title":"On minimum t-claw deletion in split graphs","authors":"Sounaka Mishra","doi":"10.1007/s00236-025-00482-2","DOIUrl":"10.1007/s00236-025-00482-2","url":null,"abstract":"<div><p>For <span>(tge 3)</span>, <span>(K_{1, t})</span> is called <i>t</i>-claw. A graph <span>(G=(V, E))</span> is <i>t</i>-claw free if it does not contain <i>t</i>-claw as a vertex-induced subgraph. In minimum <i>t</i>-claw deletion problem (<span>Min-</span><i>t</i>-<span>Claw-Del</span>), given a graph <span>(G=(V, E))</span>, it is required to find a vertex set <i>S</i> of minimum size such that <span>(G[Vsetminus S])</span> is <i>t</i>-claw free. In a split graph, the vertex set is partitioned into two sets such that one forms a clique and the other forms an independent set. Every <i>t</i>-claw in a split graph has a center vertex in the clique partition. This observation motivates us to consider the minimum one-sided bipartite <i>t</i>-claw deletion problem (<span>Min-</span><i>t</i><span>-OSBCD</span>). Given a bipartite graph <span>(G=(A cup B, E))</span>, in <span>Min-</span><i>t</i><span>-OSBCD</span> it is asked to find a vertex set <i>S</i> of minimum size such that <span>(G[(A cup B) {setminus } S])</span> has no <i>t</i>-claw with the center vertex in <i>A</i>. A primal-dual algorithm approximates <span>Min-</span><i>t</i><span>-OSBCD</span> within a factor of <i>t</i>. We prove that it is <span>({textsf{UGC}})</span>-hard to approximate with a factor better than <i>t</i>. We also prove it is approximable within a factor of 2 for dense bipartite graphs. By using these results on <span>Min-</span><i>t</i><span>-OSBCD</span>, we prove that <span>Min-</span><i>t</i>-<span>Claw-Del</span> is <span>({textsf{UGC}})</span>-hard to approximate within a factor better than <i>t</i>, for split graphs. We also consider their complementary maximization problems and prove that they are <span>({textsf{APX}})</span>-complete.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489619","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}

{"title":"On the piecewise complexity of words","authors":"Philippe Schnoebelen,&nbsp;Isa Vialard","doi":"10.1007/s00236-025-00480-4","DOIUrl":"10.1007/s00236-025-00480-4","url":null,"abstract":"<div><p>The piecewise complexity <i>h</i>(<i>u</i>) of a word is the minimal length of subwords needed to exactly characterise <i>u</i>. Its piecewise minimality index <span>(rho (u))</span> is the smallest length <i>k</i> such that <i>u</i> is minimal among its order-<i>k</i> class <span>([u]_k)</span> in Simon’s congruence. We initiate a study of these two descriptive complexity measures. Among other results, we provide efficient algorithms for computing <i>h</i>(<i>u</i>) and <span>(rho (u))</span> for a given word <i>u</i>.\u0000</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431058","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}

{"title":"Generalized straight-line programs","authors":"Gonzalo Navarro,&nbsp;Francisco Olivares,&nbsp;Cristian Urbina","doi":"10.1007/s00236-025-00481-3","DOIUrl":"10.1007/s00236-025-00481-3","url":null,"abstract":"<div><p>It was recently proved that any straight-line program (SLP) generating a given string can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We generalize this proof to a general class of grammars we call generalized SLPs (GSLPs), which allow rules of the form <span>(A rightarrow x)</span> where <i>x</i> is any Turing-complete representation (of size |<i>x</i>|) of a sequence of symbols (potentially much longer than |<i>x</i>|). We then specialize GSLPs to so-called Iterated SLPs (ISLPs), which allow rules of the form <span>(A rightarrow Pi _{i=k_1}^{k_2} B_1^{i^{c_1}}cdots B_t^{i^{c_t}})</span> of size <span>(mathcal {O}(t))</span>. We prove that ISLPs break, for some text families, the measure <span>(delta )</span> based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness. Further, ISLPs can extract any substring of length <span>(lambda )</span>, from the represented text <span>(T[1mathinner {.,.}n])</span>, in time <span>(mathcal {O}(lambda + log ^2 nlog log n))</span>. This is the first compressed representation for repetitive texts breaking <span>(delta )</span> while, at the same time, supporting direct access to arbitrary text symbols in polylogarithmic time. We also show how to compute some substring queries, like range minima and next/previous smaller value, in time <span>(mathcal {O}(log ^2 n log log n))</span>. Finally, we further specialize the grammars to run-length SLPs (RLSLPs), which restrict the rules allowed by ISLPs to the form <span>(A rightarrow B^t)</span>. Apart from inheriting all the previous results with the term <span>(log ^2 n log log n)</span> reduced to the near-optimal <span>(log n)</span>, we show that RLSLPs can exploit balancedness to efficiently compute a wide class of substring queries we call “composable”—i.e., <span>(f(X cdot Y))</span> can be obtained from <i>f</i>(<i>X</i>) and <i>f</i>(<i>Y</i>). As an example, we show how to compute Karp-Rabin fingerprints of texts substrings in <span>(mathcal {O}(log n))</span> time. While the results on RLSLPs were already known, ours are much simpler and require little precomputation time and extra data associated with the grammar.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404243","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}