Pub Date : 2025-05-05DOI: 10.1016/j.ipl.2025.106582
Olivier Rioul , Patrick Solé
The Chernoff bound is a well-known upper bound on the tail of binomial distributions of parameter 1/2 involving the binary entropy function. Hoeffding's inequality (or the Chernoff-Hoeffding inequality) is a generalization for binomial distributions of parameter , involving the q-ary entropy function (with ), which can be written in terms of the Kullback-Leibler divergence and is related to the bound in Fano's inequality. We give an information theoretic proof of that bound, and sketch some applications to channel and source coding. We also derive a refined bound which is always sharper.
{"title":"An information theoretic proof of the Chernoff-Hoeffding inequality","authors":"Olivier Rioul , Patrick Solé","doi":"10.1016/j.ipl.2025.106582","DOIUrl":"10.1016/j.ipl.2025.106582","url":null,"abstract":"<div><div>The Chernoff bound is a well-known upper bound on the tail of binomial distributions of parameter 1/2 involving the binary entropy function. Hoeffding's inequality (or the Chernoff-Hoeffding inequality) is a generalization for binomial distributions of parameter <span><math><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>q</mi></math></span>, involving the <em>q</em>-ary entropy function (with <span><math><mi>q</mi><mo>≥</mo><mn>2</mn></math></span>), which can be written in terms of the Kullback-Leibler divergence and is related to the bound in Fano's inequality. We give an information theoretic proof of that bound, and sketch some applications to channel and source coding. We also derive a refined bound which is always sharper.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106582"},"PeriodicalIF":0.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143911475","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 : 2025-04-15DOI: 10.1016/j.ipl.2025.106581
Jittat Fakcharoenphol , Nonthaphat Wongwattanakij
For any , Laue and Matijević [CCCG'07, IPL'08] give a PTAS for finding a -approximate solution to the k-hop MST problem in the Euclidean plane that runs in time . In this paper, we present an algorithm that runs in time . This gives an improvement on the dependency on k on the exponent, while having a worse dependency on ϵ. As in Laue and Matijević, we follow the framework introduced by Arora for Euclidean TSP. Our key ingredients include exponential distance scaling and compression of dynamic programming state tables.
{"title":"A PTAS for k-hop MST on the Euclidean plane: Improving dependency on k","authors":"Jittat Fakcharoenphol , Nonthaphat Wongwattanakij","doi":"10.1016/j.ipl.2025.106581","DOIUrl":"10.1016/j.ipl.2025.106581","url":null,"abstract":"<div><div>For any <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span>, Laue and Matijević [CCCG'07, IPL'08] give a PTAS for finding a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></math></span>-approximate solution to the <em>k</em>-hop MST problem in the Euclidean plane that runs in time <span><math><msup><mrow><mo>(</mo><mi>n</mi><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mi>k</mi><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow></msup></math></span>. In this paper, we present an algorithm that runs in time <span><math><msup><mrow><mo>(</mo><mi>n</mi><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mi>k</mi><mo>⋅</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo></mo><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo><mo>)</mo></mrow></msup></math></span>. This gives an improvement on the dependency on <em>k</em> on the exponent, while having a worse dependency on <em>ϵ</em>. As in Laue and Matijević, we follow the framework introduced by Arora for Euclidean TSP. Our key ingredients include exponential distance scaling and compression of dynamic programming state tables.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106581"},"PeriodicalIF":0.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844295","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 : 2025-04-15DOI: 10.1016/j.ipl.2025.106580
Jianming Lin , Weize Wang , Chang-An Zhao , Yuhao Zheng
In the implementation of isogeny-based cryptographic schemes, Vélu's formulas are essential for constructing and evaluating isogenies. Bernstein et al. proposed an approach known as √élu, which computes an ℓ-isogeny at a cost of finite field operations. This paper presents two improvements to enhance the efficiency of the implementation of √élu as follows: optimizing the index system required in √élu and speeding up the computations of the sums of products used in polynomial multiplications over a finite field with characteristic p. To optimize the index system, we modify it to enhance the utilization of x-coordinates and combine it with the technique of redundant representation, which can ultimately reduce the number of -multiplications. The speedup of the sums of products is to employ two techniques: lazy reduction (abbreviated as LZYR) and generalized interleaved Montgomery multiplication (abbreviated as INTL). These techniques aim to minimize the underlying operations. We provide an optimized C and assembly implementation of √élu. For the computational cost (in terms of -multiplications) of each isogeny involved in CTIDH2048 (resp. SQIsign), exploiting our modified index system (including the combination with redundant representation) obtains a saving up to 5.78% (resp. 5.39%) compared to the previous work. In terms of the performance (reported in CPU clock cycles) of isogeny computations in CTIDH512, applying our index system combined with INTL (resp. our index system combined with LZYR) offers an improvement up to 16.05% (resp. 10.96%) compared to the previous implementation. As for executing an isogeny group action in CTIDH512, our experimental results also demonstrate a reduction of 3.73% (resp. 1.83%) clock cycles by utilizing our index system combined with INTL (resp. our index system combined with LZYR).
{"title":"Efficient Implementations of Square-root Vélu's Formulas","authors":"Jianming Lin , Weize Wang , Chang-An Zhao , Yuhao Zheng","doi":"10.1016/j.ipl.2025.106580","DOIUrl":"10.1016/j.ipl.2025.106580","url":null,"abstract":"<div><div>In the implementation of isogeny-based cryptographic schemes, Vélu's formulas are essential for constructing and evaluating isogenies. Bernstein et al. proposed an approach known as √élu, which computes an <em>ℓ</em>-isogeny at a cost of <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msqrt><mrow><mi>ℓ</mi></mrow></msqrt><mo>)</mo></math></span> finite field operations. This paper presents two improvements to enhance the efficiency of the implementation of √élu as follows: optimizing the index system required in √élu and speeding up the computations of the sums of products used in polynomial multiplications over a finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> with characteristic <em>p</em>. To optimize the index system, we modify it to enhance the utilization of <em>x</em>-coordinates and combine it with the technique of redundant representation, which can ultimately reduce the number of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-multiplications. The speedup of the sums of products is to employ two techniques: lazy reduction (abbreviated as LZYR) and generalized interleaved Montgomery multiplication (abbreviated as INTL). These techniques aim to minimize the underlying operations. We provide an optimized C and assembly implementation of √élu. For the computational cost (in terms of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-multiplications) of each isogeny involved in CTIDH2048 (resp. SQIsign), exploiting our modified index system (including the combination with redundant representation) obtains a saving up to 5.78% (resp. 5.39%) compared to the previous work. In terms of the performance (reported in CPU clock cycles) of isogeny computations in CTIDH512, applying our index system combined with INTL (resp. our index system combined with LZYR) offers an improvement up to 16.05% (resp. 10.96%) compared to the previous implementation. As for executing an isogeny group action in CTIDH512, our experimental results also demonstrate a reduction of 3.73% (resp. 1.83%) clock cycles by utilizing our index system combined with INTL (resp. our index system combined with LZYR).</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106580"},"PeriodicalIF":0.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833606","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 : 2025-04-10DOI: 10.1016/j.ipl.2025.106579
Rodrigo Alexander Castro Campos
Given two strings of lengths m and n, with , the longest common subsequence problem consists of computing a common subsequence of maximum length by deleting symbols from both strings. While the algorithm devised in 1974 is optimal in the most general setting, algorithms that depend on parameters other than m and n have been proposed since then. In the word RAM model, let w be the word size, s be the alphabet size, d be the number of dominant symbol matches between the strings, and p be the length of the longest common subsequence. Fast algorithms for this problem have complexities , , , , , and . In this work, we present an algorithm when , and also an algorithm when which uses bitwise instructions that became recently available in modern processors.
{"title":"The longest common subsequence problem for small alphabets in the word RAM model","authors":"Rodrigo Alexander Castro Campos","doi":"10.1016/j.ipl.2025.106579","DOIUrl":"10.1016/j.ipl.2025.106579","url":null,"abstract":"<div><div>Given two strings of lengths <em>m</em> and <em>n</em>, with <span><math><mi>m</mi><mo>≤</mo><mi>n</mi></math></span>, the longest common subsequence problem consists of computing a common subsequence of maximum length by deleting symbols from both strings. While the <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>)</mo></math></span> algorithm devised in 1974 is optimal in the most general setting, algorithms that depend on parameters other than <em>m</em> and <em>n</em> have been proposed since then. In the word RAM model, let <em>w</em> be the word size, <em>s</em> be the alphabet size, <em>d</em> be the number of dominant symbol matches between the strings, and <em>p</em> be the length of the longest common subsequence. Fast algorithms for this problem have complexities <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>/</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>/</mo><mi>w</mi><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>s</mi><mo>+</mo><mi>min</mi><mo></mo><mo>(</mo><mi>p</mi><mo>(</mo><mi>n</mi><mo>−</mo><mi>p</mi><mo>)</mo><mo>,</mo><mi>p</mi><mi>m</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>s</mi><mo>+</mo><mi>d</mi><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>min</mi><mo></mo><mo>(</mo><mi>d</mi><mo>,</mo><mi>m</mi><mi>n</mi><mo>/</mo><mi>d</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>s</mi><mo>+</mo><mi>min</mi><mo></mo><mo>(</mo><mi>d</mi><mi>s</mi><mo>,</mo><mi>p</mi><mi>m</mi><mo>)</mo><mo>)</mo></math></span>, and <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>s</mi><mo>+</mo><mi>s</mi><msup><mrow><mo>!</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>s</mi><mo>+</mo><mi>d</mi><mi>log</mi><mo></mo><mi>s</mi><mo>)</mo></math></span>. In this work, we present an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>(</mo><mi>s</mi><mo>+</mo><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo></mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>min</mi><mo></mo><mo>(</mo><mi>d</mi><mi>log</mi><mo></mo><mi>s</mi><mo>,</mo><mi>p</mi><mi>m</mi><mo>)</mo><mo>)</mo></math></span> algorithm when <span><math><mi>s</mi><mo>∈</mo><mi>O</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span>, and also an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>(</mo><mi>s</mi><mo>+</mo><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo></mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>d</mi><mo>)</mo></math></span> algorithm when <span><math><mi>s</mi><mo>≤</mo><mi>w</mi></math></span> which uses bitwise instructions that became recently available in modern processors.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106579"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833605","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 : 2025-04-04DOI: 10.1016/j.ipl.2025.106578
Argyrios Deligkas, Aris Filos-Ratsikas, Alexandros A. Voudouris
{"title":"Special issue on Economics and Computation","authors":"Argyrios Deligkas, Aris Filos-Ratsikas, Alexandros A. Voudouris","doi":"10.1016/j.ipl.2025.106578","DOIUrl":"10.1016/j.ipl.2025.106578","url":null,"abstract":"","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106578"},"PeriodicalIF":0.7,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068564","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 : 2025-04-01DOI: 10.1016/j.ipl.2025.106577
George Christodoulou , Vasilis Christoforidis
We study the problem of fairly allocating indivisible goods among agents which are equipped with leveled valuation functions. Such preferences, that have been studied before in economics and fair division literature, capture a simple and intuitive economic behavior; larger bundles are always preferred to smaller ones. We provide a fine-grained analysis for various subclasses of leveled valuations focusing on two extensively studied notions of fairness, (approximate) MMS and EFX. In particular, we present a general positive result, showing the existence of 2/3-MMS allocations under valuations that are both leveled and submodular. We also show how some of our ideas can be used beyond the class of leveled valuations; for the case of two submodular (not necessarily leveled) agents we show that there always exists a 2/3-MMS allocation, complementing a recent impossibility result. Then, we switch to the case of subadditive and fractionally subadditive leveled agents, where we are able to show tight (lower and upper) bounds of 1/2 on the approximation factor of MMS. Moreover, we show the existence of exact EFX allocations under general leveled valuations via a simple protocol that in addition satisfies several natural economic properties. Finally, we take a mechanism design approach and we propose protocols that are both truthful and approximately fair under leveled valuations.
{"title":"Fair and truthful allocations under leveled valuations","authors":"George Christodoulou , Vasilis Christoforidis","doi":"10.1016/j.ipl.2025.106577","DOIUrl":"10.1016/j.ipl.2025.106577","url":null,"abstract":"<div><div>We study the problem of fairly allocating indivisible goods among agents which are equipped with <em>leveled</em> valuation functions. Such preferences, that have been studied before in economics and fair division literature, capture a simple and intuitive economic behavior; larger bundles are always preferred to smaller ones. We provide a fine-grained analysis for various subclasses of leveled valuations focusing on two extensively studied notions of fairness, (approximate) MMS and EFX. In particular, we present a general positive result, showing the existence of 2/3-MMS allocations under valuations that are both leveled and submodular. We also show how some of our ideas can be used beyond the class of leveled valuations; for the case of two submodular (not necessarily leveled) agents we show that there always exists a 2/3-MMS allocation, complementing a recent impossibility result. Then, we switch to the case of subadditive and fractionally subadditive leveled agents, where we are able to show tight (lower and upper) bounds of 1/2 on the approximation factor of MMS. Moreover, we show the existence of exact EFX allocations under general leveled valuations via a simple protocol that in addition satisfies several natural economic properties. Finally, we take a mechanism design approach and we propose protocols that are both truthful and approximately fair under leveled valuations.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106577"},"PeriodicalIF":0.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768168","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}
Pub Date : 2025-03-18DOI: 10.1016/j.ipl.2025.106576
Luis Sánchez-Fernández
The Method of Equal Shares (ES) is a popular approval-based multi-winner voting rule, which was originally proposed by Peters and Skowron. It satisfies several well-known representation axioms, like extended justified representation (EJR) and priceability, and it can be computed in polynomial time. Further, it has already been employed in several real participatory budgeting elections. In this note, we prove that ES is an instance of the EJR-Exact family of voting rules that also satisfy EJR and were proposed by Aziz et al. 2018 before the work of Peters and Skowron.
{"title":"A note on the method of equal shares","authors":"Luis Sánchez-Fernández","doi":"10.1016/j.ipl.2025.106576","DOIUrl":"10.1016/j.ipl.2025.106576","url":null,"abstract":"<div><div>The Method of Equal Shares (ES) is a popular approval-based multi-winner voting rule, which was originally proposed by Peters and Skowron. It satisfies several well-known representation axioms, like extended justified representation (EJR) and priceability, and it can be computed in polynomial time. Further, it has already been employed in several real participatory budgeting elections. In this note, we prove that ES is an instance of the EJR-Exact family of voting rules that also satisfy EJR and were proposed by Aziz et al. 2018 before the work of Peters and Skowron.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106576"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682684","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}
Pub Date : 2025-03-18DOI: 10.1016/j.ipl.2025.106575
Alexander Dobler
In 2011, Harrigan and Healy claimed that one-sided crossing minimization can be solved in polynomial time on trees [1]. We point out a counterexample to their claims, and show that one-sided crossing minimization is -hard for trees.
{"title":"A note on the complexity of one-sided crossing minimization of trees","authors":"Alexander Dobler","doi":"10.1016/j.ipl.2025.106575","DOIUrl":"10.1016/j.ipl.2025.106575","url":null,"abstract":"<div><div>In 2011, Harrigan and Healy claimed that one-sided crossing minimization can be solved in polynomial time on trees <span><span>[1]</span></span>. We point out a counterexample to their claims, and show that one-sided crossing minimization is <figure><img></figure>-hard for trees.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106575"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682683","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}
Pub Date : 2025-03-10DOI: 10.1016/j.ipl.2025.106574
Takashi Ishizuka
One of the most famous TFNP subclasses is PPP, which is the set of all search problems whose totality is guaranteed by the pigeonhole principle. The author's recent preprint [1] has introduced a TFNP problem related to the pigeonhole principle over a quotient set, called Quotient Pigeon, and shown that the problem Quotient Pigeon is not only PPP-hard but also PLS-hard. In this paper, we formulate other computational problems related to the pigeonhole principle over a quotient set via an explicit representation of the equivalence classes. Our new formulation introduces a non-trivial -complete problem for every . Furthermore, we consider the computational complexity of a computational problem related to Kőnig's lemma, which is a weaker variant of the problem formulated by Pasarkar et al. [2]. We show that our weaker variant is PPAD-hard and is in .
{"title":"On the complexity of some restricted variants of Quotient Pigeon and a weak variant of Kőnig","authors":"Takashi Ishizuka","doi":"10.1016/j.ipl.2025.106574","DOIUrl":"10.1016/j.ipl.2025.106574","url":null,"abstract":"<div><div>One of the most famous <span>TFNP</span> subclasses is <span>PPP</span>, which is the set of all search problems whose totality is guaranteed by the pigeonhole principle. The author's recent preprint <span><span>[1]</span></span> has introduced a <span>TFNP</span> problem related to the pigeonhole principle over a quotient set, called <span>Quotient Pigeon</span>, and shown that the problem <span>Quotient Pigeon</span> is not only <span>PPP</span>-hard but also <span>PLS</span>-hard. In this paper, we formulate other computational problems related to the pigeonhole principle over a quotient set via an explicit representation of the equivalence classes. Our new formulation introduces a non-trivial <span><math><mtext>PPP</mtext><mo>∩</mo><msub><mrow><mtext>PPA</mtext></mrow><mrow><mi>k</mi></mrow></msub></math></span>-complete problem for every <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>. Furthermore, we consider the computational complexity of a computational problem related to Kőnig's lemma, which is a weaker variant of the problem formulated by Pasarkar et al. <span><span>[2]</span></span>. We show that our weaker variant is <span>PPAD</span>-hard and is in <span><math><mtext>PPP</mtext><mo>∩</mo><mtext>PPA</mtext></math></span>.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106574"},"PeriodicalIF":0.7,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601479","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}
Pub Date : 2025-03-03DOI: 10.1016/j.ipl.2025.106573
Chao Yang , Zhujun Zhang
The friends-and-strangers problem is defined on two graphs X and Y of the same order n, where X is the location graph on a set of locations and Y is the friendship graph on a set of people . A configuration is a bijection from to , representing an arrangement of n people at n locations. The friends-and-stranger problem investigates the connectivity of two arbitrary configurations by a sequence of swaps of two people that are neighbors (i.e., adjacent in X) and friends (i.e., adjacent in Y). In this paper, we show that the friends-and-strangers problem with subcubic planar location graphs X is PSPACE-complete by a reduction from the Ncl (non-deterministic constraint logic) problem.
{"title":"Friends-and-strangers is PSPACE-complete","authors":"Chao Yang , Zhujun Zhang","doi":"10.1016/j.ipl.2025.106573","DOIUrl":"10.1016/j.ipl.2025.106573","url":null,"abstract":"<div><div>The friends-and-strangers problem is defined on two graphs <em>X</em> and <em>Y</em> of the same order <em>n</em>, where <em>X</em> is the location graph on a set of locations <span><math><mi>V</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> and <em>Y</em> is the friendship graph on a set of people <span><math><mi>V</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>. A configuration is a bijection from <span><math><mi>V</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> to <span><math><mi>V</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>, representing an arrangement of <em>n</em> people at <em>n</em> locations. The friends-and-stranger problem investigates the connectivity of two arbitrary configurations by a sequence of swaps of two people that are neighbors (i.e., adjacent in <em>X</em>) and friends (i.e., adjacent in <em>Y</em>). In this paper, we show that the friends-and-strangers problem with subcubic planar location graphs <em>X</em> is <span>PSPACE</span>-complete by a reduction from the <span>Ncl</span> (non-deterministic constraint logic) problem.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106573"},"PeriodicalIF":0.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534766","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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