The Hospital Residents setting models important problems like school choice, assignment of undergraduate students to degree programs, among many others. In this setting, fixed quotas are associated with the programs that limit the number of agents that can be assigned to them. Motivated by scenarios where all agents must be matched, we propose and study a generalized capacity planning problem, which allows cost-controlled flexibility with respect to quotas.
Our setting is an extension of the Hospital Resident setting where programs have the usual quota as well as an associated cost, indicating the cost of matching an agent beyond the initial quotas. We seek to compute a matching that matches all agents and is optimal with respect to preferences, and minimizes either a local or a global objective on cost.
We show that there is a sharp contrast – minimizing the local objective is polynomial-time solvable, whereas minimizing the global objective is -hard. On the positive side, we present approximation algorithms for the global objective in the general case and a particular hard case. We achieve the approximation guarantee for the special hard case via a linear programming based algorithm. We strengthen the -hardness by showing a matching lower bound to our algorithmic result.
{"title":"Generalized capacity planning for the hospital-Residents problem","authors":"Haricharan Balasundaram , Girija Limaye , Meghana Nasre , Abhinav Raja","doi":"10.1016/j.tcs.2026.115760","DOIUrl":"10.1016/j.tcs.2026.115760","url":null,"abstract":"<div><div>The Hospital Residents setting models important problems like school choice, assignment of undergraduate students to degree programs, among many others. In this setting, fixed quotas are associated with the programs that limit the number of agents that can be assigned to them. Motivated by scenarios where <em>all</em> agents must be matched, we propose and study a generalized capacity planning problem, which allows cost-controlled flexibility with respect to quotas.</div><div>Our setting is an extension of the Hospital Resident setting where programs have the usual quota as well as an associated cost, indicating the cost of matching an agent beyond the initial quotas. We seek to compute a matching that matches all agents and is optimal with respect to preferences, and minimizes either a local or a global objective on cost.</div><div>We show that there is a sharp contrast – minimizing the local objective is polynomial-time solvable, whereas minimizing the global objective is <span><math><mi>NP</mi></math></span>-hard. On the positive side, we present approximation algorithms for the global objective in the general case and a particular hard case. We achieve the approximation guarantee for the special hard case via a linear programming based algorithm. We strengthen the <span><math><mi>NP</mi></math></span>-hardness by showing a matching lower bound to our algorithmic result.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1067 ","pages":"Article 115760"},"PeriodicalIF":1.0,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080048","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 : 2026-01-14DOI: 10.1016/j.tcs.2026.115755
Ilkka Törmä
A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We investigate the existence of countable covers for gap width shifts, where the number of nonzero symbols in a configuration is bounded by a function of the minimum distance between two such symbols. As our main results, we characterize those one-dimensional gap width shifts whose two-dimensional lift is a countably covered sofic shift, and show that a large class of two-dimensional gap width shifts are countably covered.
{"title":"On countable SFT covers of sparse multidimensional shift spaces","authors":"Ilkka Törmä","doi":"10.1016/j.tcs.2026.115755","DOIUrl":"10.1016/j.tcs.2026.115755","url":null,"abstract":"<div><div>A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We investigate the existence of countable covers for gap width shifts, where the number of nonzero symbols in a configuration is bounded by a function of the minimum distance between two such symbols. As our main results, we characterize those one-dimensional gap width shifts whose two-dimensional lift is a countably covered sofic shift, and show that a large class of two-dimensional gap width shifts are countably covered.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115755"},"PeriodicalIF":1.0,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038909","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 : 2026-01-13DOI: 10.1016/j.tcs.2026.115761
Ran Hu , Divy H. Kanani , Jingru Zhang
In this paper, we consider the (weighted) one-center problem of uncertain points on cactus graphs. Given are a cactus graph G and a set of n uncertain points. Each uncertain point has m possible locations on G with probabilities and a non-negative weight. The (weighted) one-center problem aims to compute a point (the center) x* on G to minimize the maximum (weighted) expected distance from x* to all uncertain points. No previous algorithms are known for this problem. In this paper, we propose an -time algorithm for solving it. Since the input size is , our algorithm is almost optimal.
{"title":"Computing the center of uncertain points on cactus graphs","authors":"Ran Hu , Divy H. Kanani , Jingru Zhang","doi":"10.1016/j.tcs.2026.115761","DOIUrl":"10.1016/j.tcs.2026.115761","url":null,"abstract":"<div><div>In this paper, we consider the (weighted) one-center problem of uncertain points on cactus graphs. Given are a cactus graph <em>G</em> and a set of <em>n</em> uncertain points. Each uncertain point has <em>m</em> possible locations on <em>G</em> with probabilities and a non-negative weight. The (weighted) one-center problem aims to compute a point (the center) <em>x</em>* on <em>G</em> to minimize the maximum (weighted) expected distance from <em>x</em>* to all uncertain points. No previous algorithms are known for this problem. In this paper, we propose an <span><math><mrow><mi>O</mi><mo>(</mo><mo>|</mo><mi>G</mi><mo>|</mo><mo>+</mo><mi>m</mi><mi>n</mi><mi>log</mi><mi>m</mi><mi>n</mi><mo>)</mo></mrow></math></span>-time algorithm for solving it. Since the input size is <span><math><mrow><mi>O</mi><mo>(</mo><mo>|</mo><mi>G</mi><mo>|</mo><mo>+</mo><mi>m</mi><mi>n</mi><mo>)</mo></mrow></math></span>, our algorithm is almost optimal.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1067 ","pages":"Article 115761"},"PeriodicalIF":1.0,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993600","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 : 2026-01-12DOI: 10.1016/j.tcs.2026.115759
Thomas Dissaux, Nicolas Nisse
A path-decomposition of a graph is a sequence of subsets of V, called bags, that satisfy some connectivity properties. The length of a path-decomposition of a graph G is the greatest distance (in G) between two vertices that belong to a same bag and the pathlength, denoted by pℓ(G), of G is the smallest length of its path-decompositions. This parameter has been studied for its algorithmic applications for several classical metric problems like the minimum eccentricity shortest path problem, the line-distortion problem, etc. However, deciding if the pathlength of a graph G is at most 2 is NP-complete, and the best known approximation algorithm has a ratio 2 (there is no c-approximation with unless ). In this work, we focus on the study of the pathlength of simple sub-classes of planar graphs. We start by designing a linear-time algorithm that computes the pathlength of trees. Then, we show that the pathlength of cycles with n vertices is equal to . Our main result is a -approximation algorithm for the pathlength of outerplanar graphs. This algorithm is based on a characterization of almost optimal (of length at most ) path-decompositions of outerplanar graphs.
{"title":"Pathlength of outerplanar graphs","authors":"Thomas Dissaux, Nicolas Nisse","doi":"10.1016/j.tcs.2026.115759","DOIUrl":"10.1016/j.tcs.2026.115759","url":null,"abstract":"<div><div>A <em>path-decomposition</em> of a graph <span><math><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></math></span> is a sequence of subsets of <em>V</em>, called <em>bags</em>, that satisfy some connectivity properties. The <em>length</em> of a path-decomposition of a graph <em>G</em> is the greatest distance (in <em>G</em>) between two vertices that belong to a same bag and the <em>pathlength</em>, denoted by <em>p</em>ℓ(<em>G</em>), of <em>G</em> is the smallest length of its path-decompositions. This parameter has been studied for its algorithmic applications for several classical metric problems like the minimum eccentricity shortest path problem, the line-distortion problem, <em>etc</em>. However, deciding if the pathlength of a graph <em>G</em> is at most 2 is NP-complete, and the best known approximation algorithm has a ratio 2 (there is no <em>c</em>-approximation with <span><math><mrow><mi>c</mi><mo><</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span> unless <span><math><mrow><mi>P</mi><mo>=</mo><mi>N</mi><mi>P</mi></mrow></math></span>). In this work, we focus on the study of the pathlength of simple sub-classes of planar graphs. We start by designing a linear-time algorithm that computes the pathlength of trees. Then, we show that the pathlength of cycles with <em>n</em> vertices is equal to <span><math><mrow><mo>⌊</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>⌋</mo></mrow></math></span>. Our main result is a <span><math><mrow><mo>(</mo><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-approximation algorithm for the pathlength of outerplanar graphs. This algorithm is based on a characterization of almost optimal (of length at most <span><math><mrow><mi>p</mi><mi>ℓ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>1</mn></mrow></math></span>) path-decompositions of outerplanar graphs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115759"},"PeriodicalIF":1.0,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980987","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}
An edge-colored graph is said to be balanced if it has an equal number of edges of each color. Given a graph G whose edges are colored using two colors and a positive integer k, the objective in the Edge Balanced Connected Subgraph problem is to determine if G has a balanced connected subgraph containing at least k edges. We first show that this problem is NP-complete and remains so even if the solution is required to be a tree or a path. Then, we focus on the parameterized complexity of Edge Balanced Connected Subgraph and its variants (where the balanced subgraph is required to be a path/tree) with respect to k as the parameter. Towards this, we show that if a graph has a balanced connected subgraph/tree/path of size at least k, then it has one of size at least k and at most f(k) where f is a linear function. We use this result combined with dynamic programming algorithms based on color coding and representative sets to show that Edge Balanced Connected Subgraph and its variants are FPT. Further, using polynomial-time reductions to the Multilinear Monomial Detection problem, we give faster randomized FPT algorithms for the problems. In order to describe these reductions, we define a combinatorial object called relaxed-subgraph. We define this object in such a way that balanced connected subgraphs, trees and paths are relaxed-subgraphs with certain properties. This object is defined in the spirit of branching walks known for the Steiner Tree problem and may be of independent interest.
{"title":"Balanced substructures in bicolored graphs","authors":"P.S. Ardra , R. Krithika , Saket Saurabh , Roohani Sharma","doi":"10.1016/j.tcs.2026.115745","DOIUrl":"10.1016/j.tcs.2026.115745","url":null,"abstract":"<div><div>An edge-colored graph is said to be <em>balanced</em> if it has an equal number of edges of each color. Given a graph <em>G</em> whose edges are colored using two colors and a positive integer <em>k</em>, the objective in the <span>Edge Balanced Connected Subgraph</span> problem is to determine if <em>G</em> has a balanced connected subgraph containing at least <em>k</em> edges. We first show that this problem is <span>NP</span>-complete and remains so even if the solution is required to be a tree or a path. Then, we focus on the parameterized complexity of <span>Edge Balanced Connected Subgraph</span> and its variants (where the balanced subgraph is required to be a path/tree) with respect to <em>k</em> as the parameter. Towards this, we show that if a graph has a balanced connected subgraph/tree/path of size at least <em>k</em>, then it has one of size at least <em>k</em> and at most <em>f</em>(<em>k</em>) where <em>f</em> is a linear function. We use this result combined with dynamic programming algorithms based on <em>color coding</em> and <em>representative sets</em> to show that <span>Edge Balanced Connected Subgraph</span> and its variants are <span>FPT</span>. Further, using polynomial-time reductions to the <span>Multilinear Monomial Detection</span> problem, we give faster randomized <span>FPT</span> algorithms for the problems. In order to describe these reductions, we define a combinatorial object called <em>relaxed-subgraph</em>. We define this object in such a way that balanced connected subgraphs, trees and paths are relaxed-subgraphs with certain properties. This object is defined in the spirit of branching walks known for the <span>Steiner Tree</span> problem and may be of independent interest.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115745"},"PeriodicalIF":1.0,"publicationDate":"2026-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980988","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 : 2026-01-11DOI: 10.1016/j.tcs.2026.115754
Nicolas Bédaride , Valérie Berthé , Antoine Julien
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order, they also provide the simplest examples of quasicrystals, as tilings of the line obtained via cut and project sets with a cubical canonical window. By construction, the number of occurrences of each letter in a factor (i.e., a string of consecutive letters) of a hypercubic billiard word only depends on the length of the factor, up to an additive constant. In other words, the difference of the number of occurrences of each letter in factors of the same length is bounded. In contrast with the behaviour of letters, we prove the existence of factors that are not balanced in billiard words: the difference of the number of occurrences of such unbalanced factors in longer factors of the same length is unbounded. The proof relies both on topological methods inspired by tiling cohomology and on arithmetic results on bounded remainder sets for toral translations.
{"title":"On balance properties of hypercubic billiard words","authors":"Nicolas Bédaride , Valérie Berthé , Antoine Julien","doi":"10.1016/j.tcs.2026.115754","DOIUrl":"10.1016/j.tcs.2026.115754","url":null,"abstract":"<div><div>This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order, they also provide the simplest examples of quasicrystals, as tilings of the line obtained via cut and project sets with a cubical canonical window. By construction, the number of occurrences of each letter in a factor (i.e., a string of consecutive letters) of a hypercubic billiard word only depends on the length of the factor, up to an additive constant. In other words, the difference of the number of occurrences of each letter in factors of the same length is bounded. In contrast with the behaviour of letters, we prove the existence of factors that are not balanced in billiard words: the difference of the number of occurrences of such unbalanced factors in longer factors of the same length is unbounded. The proof relies both on topological methods inspired by tiling cohomology and on arithmetic results on bounded remainder sets for toral translations.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115754"},"PeriodicalIF":1.0,"publicationDate":"2026-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980986","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 : 2026-01-11DOI: 10.1016/j.tcs.2026.115746
Zsuzsanna Lipták , Francesco Masillo , Gonzalo Navarro
We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem can be solved in optimal time whp for the updates and worst-case time for the queries, where N is the total collection size [Gawrychowski et al., SODA 2018]. We present here a much simpler solution based on a forest of enhanced splay trees (FeST), where both the updates and the substring comparison take amortized time, n being the sum of the lengths of the strings involved in the operation. The length ℓ of the longest common prefix is computed in amortized time. Our query results are correct whp. Our simpler solution enables other more general updates in amortized time, such as reversing a substring and/or mapping its symbols. We can also make FeST use compact space, and extend it to regard substrings as circular or as their omega extension. A C++-implementation of our FeST data structure is available at https://github.com/fmasillo/FeST.
{"title":"A textbook solution for dynamic strings","authors":"Zsuzsanna Lipták , Francesco Masillo , Gonzalo Navarro","doi":"10.1016/j.tcs.2026.115746","DOIUrl":"10.1016/j.tcs.2026.115746","url":null,"abstract":"<div><div>We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem can be solved in optimal time <span><math><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mi>N</mi><mo>)</mo></mrow></math></span> whp for the updates and <span><math><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math></span> worst-case time for the queries, where <em>N</em> is the total collection size [Gawrychowski et al., SODA 2018]. We present here a much simpler solution based on a forest of enhanced splay trees (FeST), where both the updates and the substring comparison take <span><math><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mi>n</mi><mo>)</mo></mrow></math></span> amortized time, <em>n</em> being the sum of the lengths of the strings involved in the operation. The length ℓ of the longest common prefix is computed in <span><math><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mi>n</mi><mo>+</mo><msup><mi>log</mi><mn>2</mn></msup><mi>ℓ</mi><mo>)</mo></mrow></math></span> amortized time. Our query results are correct whp. Our simpler solution enables other more general updates in <span><math><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mi>n</mi><mo>)</mo></mrow></math></span> amortized time, such as reversing a substring and/or mapping its symbols. We can also make FeST use compact space, and extend it to regard substrings as circular or as their omega extension. A <span>C++</span>-implementation of our FeST data structure is available at <span><span>https://github.com/fmasillo/FeST</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115746"},"PeriodicalIF":1.0,"publicationDate":"2026-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078801","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 : 2026-01-09DOI: 10.1016/j.tcs.2026.115747
Maxime Crochemore , Costas S. Iliopoulos , Jakub Radoszewski , Wojciech Rytter , Juliusz Straszyński , Tomasz Waleń , Wiktor Zuba
Internal pattern matching requires one to answer queries about factors of a given string. Many results are known on answering internal period queries, asking for the periods of a given factor. In this paper we investigate internal queries asking for covers (also known as quasiperiods) of a given factor. Let n denote the length of the string and m denote the length of the factor in question. We propose a data structure that answers such queries in time for the shortest cover and in time for a representation of all the covers, after time and space preprocessing.
This is a full version of a conference paper at SPIRE 2020 with query complexities improved by a log log n-factor and additional applications.
{"title":"Internal quasiperiod queries","authors":"Maxime Crochemore , Costas S. Iliopoulos , Jakub Radoszewski , Wojciech Rytter , Juliusz Straszyński , Tomasz Waleń , Wiktor Zuba","doi":"10.1016/j.tcs.2026.115747","DOIUrl":"10.1016/j.tcs.2026.115747","url":null,"abstract":"<div><div>Internal pattern matching requires one to answer queries about factors of a given string. Many results are known on answering internal period queries, asking for the periods of a given factor. In this paper we investigate internal queries asking for covers (also known as quasiperiods) of a given factor. Let <em>n</em> denote the length of the string and <em>m</em> denote the length of the factor in question. We propose a data structure that answers such queries in <span><math><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mi>m</mi><mo>)</mo></mrow></math></span> time for the shortest cover and in <span><math><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mi>m</mi><mi>log</mi><mi>log</mi><mi>m</mi><mo>)</mo></mrow></math></span> time for a representation of all the covers, after <span><math><mrow><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mi>n</mi><mo>)</mo></mrow></math></span> time and space preprocessing.</div><div>This is a full version of a conference paper at SPIRE 2020 with query complexities improved by a log log <em>n</em>-factor and additional applications.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115747"},"PeriodicalIF":1.0,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980990","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 : 2026-01-07DOI: 10.1016/j.tcs.2026.115744
Zi-Yuan Liu , Masahiro Mambo , Raylin Tso , Yi-Fan Tseng
In this study, we revisit the cryptosystem termed public-key encryption with filtered equality test (PKEFET), originally devised by Huang et al. (J. Comput. Syst. Sci. 2017) and subsequently refined by Chen et al. (Des. Codes Cryptogr. 2021). This notion allows users to delegate the equality test functionality of ciphertexts to a tester, but only for ciphertexts associated with a selected message set. More specifically, consider two ciphertexts related to plaintexts m and m′, along with their respective tokens related to two plaintext sets m and m′. Assuming m ∈ m and m′ ∈ m′ hold simultaneously, then any tester has the ability to determine if the ciphertexts are associated with an identical plaintext (i.e., ). With this functionality, PKEFET is valuable in applications such as encrypted data search and spam filtering. However, there exist several challenges in the current PKEFET schemes, such as: (i) security is limited to indistinguishability against “non-adaptive” chosen-ciphertext attacks (CCA1) and (ii) the computational and storage complexities scale linearly with the maximum number of plaintexts that a token can authenticate. To address these challenges, by employing public-key encryption and key-policy attribute-based encryption (KPABE) supporting OR-gate policies as the foundational building blocks, we propose a generic construction of PKEFET. In particular, we show that the required KPABE can be obtained from identity-based encryption. We demonstrate that the proposed construction satisfies one-wayness and indistinguishability under strong filtered equality test against adaptive chosen-ciphertext attacks (CCA2). Moreover, the resulting scheme has significant computational and storage complexity advantages compared to existing PKEFET schemes.
{"title":"Public-key encryption with filtered equality test against adaptive chosen-ciphertext attacks","authors":"Zi-Yuan Liu , Masahiro Mambo , Raylin Tso , Yi-Fan Tseng","doi":"10.1016/j.tcs.2026.115744","DOIUrl":"10.1016/j.tcs.2026.115744","url":null,"abstract":"<div><div>In this study, we revisit the cryptosystem termed public-key encryption with filtered equality test (PKEFET), originally devised by Huang et al. (<em>J. Comput. Syst. Sci.</em> 2017) and subsequently refined by Chen et al. (<em>Des. Codes Cryptogr.</em> 2021). This notion allows users to delegate the equality test functionality of ciphertexts to a tester, but only for ciphertexts associated with a selected message set. More specifically, consider two ciphertexts related to plaintexts <em>m</em> and <em>m</em>′, along with their respective tokens related to two plaintext sets <strong><em>m</em></strong> and <strong><em>m</em></strong>′. Assuming <em>m</em> ∈ <strong><em>m</em></strong> and <em>m</em>′ ∈ <strong><em>m</em></strong>′ hold simultaneously, then any tester has the ability to determine if the ciphertexts are associated with an identical plaintext (i.e., <span><math><mrow><mi>m</mi><mo>=</mo><msup><mi>m</mi><mo>′</mo></msup></mrow></math></span>). With this functionality, PKEFET is valuable in applications such as encrypted data search and spam filtering. However, there exist several challenges in the current PKEFET schemes, such as: (i) security is limited to indistinguishability against “non-adaptive” chosen-ciphertext attacks (CCA1) and (ii) the computational and storage complexities scale linearly with the maximum number of plaintexts that a token can authenticate. To address these challenges, by employing public-key encryption and key-policy attribute-based encryption (KPABE) supporting OR-gate policies as the foundational building blocks, we propose a generic construction of PKEFET. In particular, we show that the required KPABE can be obtained from identity-based encryption. We demonstrate that the proposed construction satisfies one-wayness and indistinguishability under strong filtered equality test against adaptive chosen-ciphertext attacks (CCA2). Moreover, the resulting scheme has significant computational and storage complexity advantages compared to existing PKEFET schemes.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1067 ","pages":"Article 115744"},"PeriodicalIF":1.0,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080049","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 : 2026-01-07DOI: 10.1016/j.tcs.2026.115743
Thomas W. Cusick , Younhwan Cheon
A Boolean function gn in n variables is rotation symmetric (RS) if it is invariant under powers of . An RS function is monomial rotation symmetric (MRS) if it is generated by applying powers of ρ to a single monomial, say where d is the degree of the function. An MRS function in n variables is called truncated rotation symmetric (TRS) if the function stops the expansion for the n-variable MRS function at the term where xn first occurs. Truncated functions are important because they are used in the computation of linear recursions which the weights of any RS functions are known to satisfy. Computing these recursions in general is very complex. This paper proves that for the quadratic TRS functions, an explicit formula for the generating function for the weights can be proved. This removes the need for the complex computation and makes the weight computation much simpler.
{"title":"Quadratic truncated rotation symmetric Boolean functions","authors":"Thomas W. Cusick , Younhwan Cheon","doi":"10.1016/j.tcs.2026.115743","DOIUrl":"10.1016/j.tcs.2026.115743","url":null,"abstract":"<div><div>A Boolean function <em>g<sub>n</sub></em> in <em>n</em> variables is rotation symmetric (RS) if it is invariant under powers of <span><math><mrow><mi>ρ</mi><mrow><mo>(</mo><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>x</mi><mi>n</mi></msub><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><msub><mi>x</mi><mn>2</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>x</mi><mi>n</mi></msub><mo>,</mo><msub><mi>x</mi><mn>1</mn></msub><mo>)</mo></mrow></mrow></math></span>. An RS function is monomial rotation symmetric (MRS) if it is generated by applying powers of <em>ρ</em> to a single monomial, say <span><math><mrow><msub><mi>x</mi><mn>1</mn></msub><msub><mi>x</mi><mrow><mi>a</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msub><mo>…</mo><msub><mi>x</mi><mrow><mi>a</mi><mo>(</mo><mi>d</mi><mo>)</mo></mrow></msub><mo>,</mo></mrow></math></span> where <em>d</em> is the degree of the function. An MRS function in <em>n</em> variables is called truncated rotation symmetric (TRS) if the function stops the expansion for the <em>n</em>-variable MRS function at the term where <em>x<sub>n</sub></em> first occurs. Truncated functions are important because they are used in the computation of linear recursions which the weights of any RS functions are known to satisfy. Computing these recursions in general is very complex. This paper proves that for the quadratic TRS functions, an explicit formula for the generating function for the weights can be proved. This removes the need for the complex computation and makes the weight computation much simpler.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1066 ","pages":"Article 115743"},"PeriodicalIF":1.0,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928841","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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