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Extending Partial Representations of Circle Graphs in Near-Linear Time 在近线性时间内扩展圆图的部分表示法

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-26 DOI: 10.1007/s00453-024-01216-5

Guido Brückner, Ignaz Rutter, Peter Stumpf

{"title":"Extending Partial Representations of Circle Graphs in Near-Linear Time","authors":"Guido Brückner, Ignaz Rutter, Peter Stumpf","doi":"10.1007/s00453-024-01216-5","DOIUrl":"10.1007/s00453-024-01216-5","url":null,"abstract":"<div>The partial representation extension problem generalizes the recognition problem for geometric intersection graphs. The input consists of a graph G, a subgraph (H subseteq G) and a representation (mathcal R') of H. The question is whether G admits a representation (mathcal R) whose restriction to H is (mathcal R'). We study this question for circle graphs, which are intersection graphs of chords of a circle. Their representations are called chord diagrams. We show that for a graph with n vertices and m edges the partial representation extension problem can be solved in (O((n + m) alpha (n + m))) time, thereby improving over an (O(n^3))-time algorithm by Chaplick et al. (J Graph Theory 91(4), 365–394, 2019). The main technical contributions are a canonical way of orienting chord diagrams and a novel compact representation of the set of all canonically oriented chord diagrams that represent a given circle graph G, which is of independent interest.</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 7","pages":"2152 - 2173"},"PeriodicalIF":0.9,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01216-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312141","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

(alpha _i)-Metric Graphs: Radius, Diameter and all Eccentricities $$alpha _i$$ -度量图形：半径、直径和所有偏心率

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-25 DOI: 10.1007/s00453-024-01223-6

Feodor F. Dragan, Guillaume Ducoffe

{"title":"(alpha _i)-Metric Graphs: Radius, Diameter and all Eccentricities","authors":"Feodor F. Dragan, Guillaume Ducoffe","doi":"10.1007/s00453-024-01223-6","DOIUrl":"10.1007/s00453-024-01223-6","url":null,"abstract":"<div>We extend known results on chordal graphs and distance-hereditary graphs to much larger graph classes by using only a common metric property of these graphs. Specifically, a graph is called (alpha _i)-metric ((iin {mathcal {N}})) if it satisfies the following (alpha _i)-metric property for every vertices u, w, v and x: if a shortest path between u and w and a shortest path between x and v share a terminal edge vw, then (d(u,x)ge d(u,v) + d(v,x)-i). Roughly, gluing together any two shortest paths along a common terminal edge may not necessarily result in a shortest path but yields a “near-shortest” path with defect at most i. It is known that (alpha _0)-metric graphs are exactly ptolemaic graphs, and that chordal graphs and distance-hereditary graphs are (alpha _i)-metric for (i=1) and (i=2), respectively. We show that an additive O(i)-approximation of the radius, of the diameter, and in fact of all vertex eccentricities of an (alpha _i)-metric graph can be computed in total linear time. Our strongest results are obtained for (alpha _1)-metric graphs, for which we prove that a central vertex can be computed in subquadratic time, and even better in linear time for so-called ((alpha _1,varDelta ))-metric graphs (a superclass of chordal graphs and of plane triangulations with inner vertices of degree at least 7). The latter answers a question raised in Dragan (Inf Probl Lett 154:105873, 2020), 2020). Our algorithms follow from new results on centers and metric intervals of (alpha _i)-metric graphs. In particular, we prove that the diameter of the center is at most (3i+2) (at most 3, if (i=1)). The latter partly answers a question raised in Yushmanov and Chepoi (Math Probl Cybernet 3:217–232, 1991).</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 7","pages":"2092 - 2129"},"PeriodicalIF":0.9,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01223-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303258","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

On The Closures of Monotone Algebraic Classes and Variants of the Determinant 论单调代数类的闭包和判定式的变体

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-25 DOI: 10.1007/s00453-024-01221-8

Prasad Chaugule, Nutan Limaye

{"title":"On The Closures of Monotone Algebraic Classes and Variants of the Determinant","authors":"Prasad Chaugule, Nutan Limaye","doi":"10.1007/s00453-024-01221-8","DOIUrl":"10.1007/s00453-024-01221-8","url":null,"abstract":"<div>In this paper we prove the following two results.<ul>\u0000 <li>\u0000 We show that for any (C in {textsf {mVF}, textsf {mVP}, textsf {mVNP}}), (C = overline{C}). Here, (textsf {mVF}, textsf {mVP}), and (textsf {mVNP}) are monotone variants of (textsf {VF}, textsf {VP}), and (textsf {VNP}), respectively. For an algebraic complexity class C, (overline{C}) denotes the closure of C. For (textsf {mVBP}) a similar result was shown in Bläser et al. (in: 35th Computational Complexity Conference, CCC 2020. LIPIcs, vol 169, pp 21–12124, 2020. https://doi.org/10.4230/LIPIcs.CCC.2020.21). Here we extend their result by adapting their proof.\u0000 </li>\u0000 <li>\u0000 We define polynomial families ({mathcal {P}(k)_n}_{n ge 0}), such that ({mathcal {P}(0)_n}_{n ge 0}) equals the determinant polynomial. We show that ({mathcal {P}(k)_n}_{n ge 0}) is (textsf {VBP}) complete for (k=1) and it becomes (textsf {VNP}) complete when (k ge 2). In particular, ({mathcal {P}(k)_n}) is (mathtt {Det^{ne k}_n(X)}), a polynomial obtained by summing over all signed cycle covers that avoid length k cycles. We show that (mathtt {Det^{ne 1}_n(X)}) is complete for (textsf {VBP}) and (mathtt {Det^{ne k}_n(X)}) is complete for (textsf {VNP}) for all (k ge 2) over any field (mathbb {F}).\u0000 </li>\u0000 </ul></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 7","pages":"2130 - 2151"},"PeriodicalIF":0.9,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303306","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}

引用次数: 0

Embedding Arbitrary Boolean Circuits into Fungal Automata 将任意布尔电路嵌入真菌自动机

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-21 DOI: 10.1007/s00453-024-01222-7

Augusto Modanese, Thomas Worsch

引用次数: 0

The Near Exact Bin Covering Problem 近乎精确的垃圾箱覆盖问题

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-19 DOI: 10.1007/s00453-024-01224-5

Asaf Levin

引用次数: 0

Diverse Pairs of Matchings 多样化的配对

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-15 DOI: 10.1007/s00453-024-01214-7

Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, Danil Sagunov

引用次数: 0

Linear Space Data Structures for Finite Groups with Constant Query-Time 查询时间不变的有限群线性空间数据结构

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-11 DOI: 10.1007/s00453-024-01212-9

Bireswar Das, Anant Kumar, Shivdutt Sharma, Dhara Thakkar

{"title":"Linear Space Data Structures for Finite Groups with Constant Query-Time","authors":"Bireswar Das, Anant Kumar, Shivdutt Sharma, Dhara Thakkar","doi":"10.1007/s00453-024-01212-9","DOIUrl":"10.1007/s00453-024-01212-9","url":null,"abstract":"<div>A finite group of order n can be represented by its Cayley table. In the word-RAM model the Cayley table of a group of order n can be stored using (O(n^2)) words and can be used to answer a multiplication query in constant time. It is interesting to ask if we can design a data structure to store a group of order n that uses (o(n^2)) space but can still answer a multiplication query in constant time. Das et al. (J Comput Syst Sci 114:137–146, 2020) showed that for any finite group G of order n and for any (delta in [1/log {n}, 1]), a data structure can be constructed for G that uses (O(n^{1+delta }/delta )) space and answers a multiplication query in time (O(1/delta )). Farzan and Munro (ISSAC, 2006) gave an information theoretic lower bound of (Omega (n)) on the number of words to store a group of order n. We design a constant query-time data structure that can store any finite group using O(n) words where n is the order of the group. Since our data structure achieves the information theoretic lower bound and answers queries in constant time, it is optimal in both space usage and query-time. A crucial step in the process is essentially to design linear space and constant query-time data structures for nonabelian simple groups. The data structures for nonabelian simple groups are designed using a lemma that we prove using the Classification Theorem for Finite Simple Groups.</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 6","pages":"1979 - 2025"},"PeriodicalIF":0.9,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097564","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}

引用次数: 0

Pattern Masking for Dictionary Matching: Theory and Practice 用于字典匹配的模式屏蔽：理论与实践

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-06 DOI: 10.1007/s00453-024-01213-8

Panagiotis Charalampopoulos, Huiping Chen, Peter Christen, Grigorios Loukides, Nadia Pisanti, Solon P. Pissis, Jakub Radoszewski

{"title":"Pattern Masking for Dictionary Matching: Theory and Practice","authors":"Panagiotis Charalampopoulos, Huiping Chen, Peter Christen, Grigorios Loukides, Nadia Pisanti, Solon P. Pissis, Jakub Radoszewski","doi":"10.1007/s00453-024-01213-8","DOIUrl":"10.1007/s00453-024-01213-8","url":null,"abstract":"<div>Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching (PMDM) problem: given a dictionary (mathscr {D}) of d strings, each of length (ell ), a query string q of length (ell ), and a positive integer z, we are asked to compute a smallest set (Ksubseteq {1,ldots ,ell }), so that if q[i] is replaced by a wildcard for all (iin K), then q matches at least z strings from (mathscr {D}). Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k-Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial (mathscr {O}((dell )^{|K|/3}+dell ))-time and (mathscr {O}(dell ))-space algorithm for PMDM for (|K|=mathscr {O}(1)). In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k-Clique hypothesis fails (Abboud et al. in SIAM J Comput 47:2527–2555, 2018; Lincoln et al., in: 29th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018). Our combinatorial algorithm, executed with small |K|, is the backbone of a greedy heuristic that we propose. Our experiments on real-world and synthetic datasets show that our heuristic finds nearly-optimal solutions in practice and is also very efficient. We also generalize this algorithm for the problem of masking multiple query strings simultaneously so that every string has at least z matches in (mathscr {D}). PMDM can be viewed as a generalization of the decision version of the dictionary matching with mismatches problem: by querying a PMDM data structure with string q and (z=1), one obtains the minimal number of mismatches of q with any string from (mathscr {D}). The query time or space of all known data structures for the more restricted problem of dictionary matching with at most k mismatches incurs some exponential factor with respect to k. A simple exact algorithm for PMDM runs in time (mathscr {O}(2^ell d)). We present a data structure for PMDM that answers queries over (mathscr {D}) in time (mathscr {O}(2^{ell /2}(2^{ell /2}+tau )ell )) and requires space (mathscr {O}(2^{ell }d^2/tau ^2+2^{ell /2}d)), for any parameter (tau in [1,d]). We complement our results by showing a two-way polynomial-time reduction ","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 6","pages":"1948 - 1978"},"PeriodicalIF":0.9,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01213-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055360","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

Finding Optimal Solutions with Neighborly Help 在邻居的帮助下找到最佳解决方案

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-06 DOI: 10.1007/s00453-023-01204-1

Elisabet Burjons, Fabian Frei, Edith Hemaspaandra, Dennis Komm, David Wehner

{"title":"Finding Optimal Solutions with Neighborly Help","authors":"Elisabet Burjons, Fabian Frei, Edith Hemaspaandra, Dennis Komm, David Wehner","doi":"10.1007/s00453-023-01204-1","DOIUrl":"10.1007/s00453-023-01204-1","url":null,"abstract":"<div>Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighbor instances, that is, instances with one local modification? For example, can we efficiently compute an optimal coloring for a graph from optimal colorings for all one-edge-deleted subgraphs? Studying such questions not only gives detailed insight into the structure of the problem itself, but also into the complexity of related problems, most notably, graph theory’s core notion of critical graphs (e.g., graphs whose chromatic number decreases under deletion of an arbitrary edge) and the complexity-theoretic notion of minimality problems (also called criticality problems, e.g., recognizing graphs that become 3-colorable when an arbitrary edge is deleted). We focus on two prototypical graph problems, colorability and vertex cover. For example, we show that it is (text {NP})-hard to compute an optimal coloring for a graph from optimal colorings for all its one-vertex-deleted subgraphs, and that this remains true even when optimal solutions for all one-edge-deleted subgraphs are given. In contrast, computing an optimal coloring from all (or even just two) one-edge-added supergraphs is in (text {P}). We observe that vertex cover exhibits a remarkably different behavior, demonstrating the power of our model to delineate problems from each other more precisely on a structural level. Moreover, we provide a number of new complexity results for minimality and criticality problems. For example, we prove that Minimal-3-UnColorability is complete for (text {DP}) (differences of (text {NP}) sets), which was previously known only for the more amenable case of deleting vertices rather than edges. For vertex cover, we show that recognizing (beta )-vertex-critical graphs is complete for (Theta _2^text {p}) (parallel access to (text {NP})), obtaining the first completeness result for a criticality problem for this class.</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 6","pages":"1921 - 1947"},"PeriodicalIF":0.9,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-023-01204-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055369","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

Preface of the Special Issue Dedicated to Selected Papers from IWOCA 2022 IWOCA 2022 论文选特刊序言

IF 0.9 4区计算机科学

Algorithmica Pub Date : 2024-03-05 DOI: 10.1007/s00453-024-01225-4

Cristina Bazgan, Henning Fernau

引用次数: 0