Theoretical Computer Science最新文献

{"title":"Packing squares independently","authors":"Wei Wu ,&nbsp;Hiroki Numaguchi ,&nbsp;Nir Halman ,&nbsp;Yannan Hu ,&nbsp;Mutsunori Yagiura","doi":"10.1016/j.tcs.2024.114910","DOIUrl":"10.1016/j.tcs.2024.114910","url":null,"abstract":"<div><div>Given a set of squares and a strip with bounded width and infinite height, we consider a square strip packaging problem, which we call the square independent packing problem (SIPP), to minimize the strip height so that all the squares are packed into independent cells separated by horizontal and vertical partitions. For the SIPP, we first investigate efficient solution representations and propose a compact representation that reduces the search space from <span><math><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>!</mo><mo>)</mo></math></span> to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, with <em>n</em> the number of given squares, while guaranteeing that there exists a solution representation that corresponds to an optimal solution. Based on the solution representation, we show that the problem is <span><math><mi>NP</mi></math></span>-hard. To solve the SIPP, we propose a dynamic programming method that can be extended to a fully polynomial-time approximation scheme (FPTAS). We also propose three mathematical programming formulations based on different solution representations and confirm their performance through computational experiments with a mathematical programming solver. Finally, we discuss several extensions that are relevant to practical applications.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114910"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441059","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":"Synergistic knowledge","authors":"Christian Cachin,&nbsp;David Lehnherr,&nbsp;Thomas Studer","doi":"10.1016/j.tcs.2024.114902","DOIUrl":"10.1016/j.tcs.2024.114902","url":null,"abstract":"<div><div>Simplicial complexes are a successful model for distributed computing. They have recently been observed to provide an interesting model for epistemic multi-agent logic where the agents' local states are the main building blocks (instead of the global states). A natural generalization is to study epistemic logic on semi-simplicial sets. However, finding the appropriate modal logic for semi-simplicial models has been an open question. We answer this by introducing the logic of synergistic knowledge and establishing its soundness and completeness.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114902"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446330","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":"Adaptive collective responses to local stimuli in anonymous dynamic networks","authors":"Shunhao Oh ,&nbsp;Dana Randall ,&nbsp;Andréa W. Richa","doi":"10.1016/j.tcs.2024.114904","DOIUrl":"10.1016/j.tcs.2024.114904","url":null,"abstract":"<div><div>We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents are represented by vertices in a dynamic graph <span><math><mi>G</mi></math></span> whose edge set changes over time, and stimuli are placed adversarially on the vertices of <span><math><mi>G</mi></math></span> where each agent is only capable of recognizing a co-located stimulus. Agents communicate via token passing along edges to alert other agents to transition to an <span>Aware</span> state when stimuli are present and an <span>Unaware</span> state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that can handle arbitrary adversarial stimulus dynamics, while an adversary (or the agents themselves) reconfigures the connections (edges) of <span><math><mi>G</mi></math></span> over time in a controlled way. This algorithm can be used to solve the <em>foraging problem</em> on reconfigurable graphs where, in addition to food sources (stimuli) being discovered, removed, or shifted arbitrarily, we would like the agents to consistently self-organize, using only local interactions, such that if the food remains in a position long enough, the agents transition to a <em>gather phase</em> in which many collectively form a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should undergo a self-induced collective phase change and switch to a <em>search phase</em> in which they distribute themselves randomly throughout the graph to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing broadcast waves of state transition that may interfere with each other. Like a physical phase change, such as the ferromagnetic models underlying the gather and search algorithms used for foraging, microscopic changes in the environment trigger these macroscopic, system-wide transitions as agents share information and respond locally to get the desired collective response.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114904"},"PeriodicalIF":0.9,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535257","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":"Dynamic path finding for multi-load agent pickup and delivery problem","authors":"Yifei Li,&nbsp;Ruixi Huang,&nbsp;Hao Ye,&nbsp;Hejiao Huang,&nbsp;Hongwei Du","doi":"10.1016/j.tcs.2024.114897","DOIUrl":"10.1016/j.tcs.2024.114897","url":null,"abstract":"<div><div>Recently, the Multi-Agent Pickup and Delivery (MAPD) problem has attracted widespread attention from both academia and industry. In the MAPD problem, each task has its pickup and delivery locations, and the agent needs to pick this task up from the pickup location and deliver it to its delivery location. Therefore, existing works consider the MAPD problem as the core problem in industrial scenarios, e.g., logistics warehouse. Note that the agents considered in the MAPD problem are single-load agents that complete tasks one by one. However, many commercial companies have deployed agents with multi-load instead of single-load agents to improve efficiency and reduce costs. The agents with multi-load can complete multiple tasks at once, so existing solutions cannot work well with the MAPD problem for multi-agents. To solve this issue, we investigate a novel problem in this paper, namely the Multi-Load Agent Pickup and Delivery (MLAPD) problem, where the agents with multi-load not only need to complete assigned real-time tasks but also need to avoid conflicts with each other and the goal is to minimize the total cost in the warehouse. To address this novel problem, we develop a task assignment to complete the assignments between multi-load agents and online tasks in real-time and a dynamic path finding problem that enables multi-load agents to move along conflict-free paths. Finally, extensive experiments in two different warehouses examine the effectiveness of our solutions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114897"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441262","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":"Approximation algorithms for finding maximum containing circle and sphere","authors":"Kaiqi Zhang ,&nbsp;Siyuan Zhang ,&nbsp;Jirun Gao ,&nbsp;Hongzhi Wang ,&nbsp;Hong Gao ,&nbsp;Jianzhong Li","doi":"10.1016/j.tcs.2024.114901","DOIUrl":"10.1016/j.tcs.2024.114901","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We first study maximum containing circle problem. The input to the problem is a weighted set of points and a circle of fixed radius, and the output is a suitable location of the circle such that the sum of the weights of the points covered by the circle is maximized. We propose a special polygon, called symmetrical rectilinear polygon (SRP). In this paper, we give a method for constructing the circumscribed SRP of a circle and prove the area relationship between this polygon and the circle. We solve the maximum containing SRP problem exactly, and based on this, give an algorithm for solving the &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-approximation of maximum containing circle problem. We also show that the algorithm is valid for most inputs. It only needs &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; time for unit points and &lt;span&gt;&lt;math&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; time for weighted points. Due to its low time complexity, the algorithm can run as a stand-alone algorithm or as a preprocessor for other algorithms. As an extension of our work, we discuss a 3D version of the unweighted maximum containing circle problem, i.e., containing the maximum number of points with a given sphere. We give a &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-approximation algorithm for this problem that returns correct results in &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mr","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114901"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434050","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":"Efficient algorithm for stochastic rumor blocking problem in social networks during safety accident period","authors":"Jianming Zhu ,&nbsp;Ye Xing ,&nbsp;Runzhi Li ,&nbsp;Smita Ghosh ,&nbsp;Priyanshi Garg ,&nbsp;Weili Wu","doi":"10.1016/j.tcs.2024.114898","DOIUrl":"10.1016/j.tcs.2024.114898","url":null,"abstract":"<div><div>Rumor sources spread negative information throughout the network, which may cause unbelievable results in real society especially for social safety field. Propagating positive information from several “protector” users is an effective method for rumor blocking once the rumor is detected. Based on the probability of each user being a rumor, “protector” nodes need to be selected in order to prepare for rumor blocking. Given a social network <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>Q</mi><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>P</mi></mrow><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></msub></math></span> is the probability that <em>v</em> is activated by <em>u</em> after <em>u</em> is activated, and <em>Q</em> is the weight function on node set <em>V</em>, <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> is the probability that <em>v</em> will be a rumor source. Stochastic Rumor Blocking (SRB) problem is to select <em>k</em> nodes as “protector” such that the expected eventually influenced users by rumor is minimized. SRB will be proved to be NP-hard and the objective function is supermodular. We present a Compound Reverse Influence Set sampling method for estimation of the objective value which can be represented as a compound set function. A randomized greedy algorithm with theoretical analysis will be presented and other two different “protector” selection strategies will be proposed for comparison. Finally, we evaluate our algorithm on real world data sets and do comparison among different strategies.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114898"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434048","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":"Dynamically equivalent disjunctive networks","authors":"Julio Aracena ,&nbsp;Luis Cabrera-Crot ,&nbsp;Adrien Richard ,&nbsp;Lilian Salinas","doi":"10.1016/j.tcs.2024.114899","DOIUrl":"10.1016/j.tcs.2024.114899","url":null,"abstract":"<div><div>The study of the dynamical behavior of Boolean networks with different update schedules has so far focused primarily on the possible dynamics and equivalent networks that can be obtained. However, few studies have been done about which networks can be obtained from another network with a non-parallel schedule.</div><div>In this article, we define the problem of finding a Boolean network that is dynamically equivalent to another network. For the general case, it is shown that the problem is NP-Hard. However, if the problem is restricted to disjunctive Boolean networks, it can be solved in polynomial time.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114899"},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535254","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":"Approximating decision trees with priority hypotheses","authors":"Jing Yuan ,&nbsp;Shaojie Tang","doi":"10.1016/j.tcs.2024.114896","DOIUrl":"10.1016/j.tcs.2024.114896","url":null,"abstract":"<div><div>This paper addresses the problem of creating decision trees for identifying hypotheses, also known as entities, in a setting where the cost of an action is dependent on the true hypothesis. Specifically, we consider the scenario where <em>n</em> hypotheses are divided into <em>m</em> groups based on their priority levels. Taking an action on a higher priority hypothesis incurs a higher cost. This is relevant to many real-world applications where cost-sensitive decisions need to be made. For example, in a medical diagnosis task, the goal is to take a series of actions (such as medical tests) to identify a cause. Each action in this process requires conducting a test on the patient and observing the outcome, which can take anywhere from a few minutes to several weeks depending on the test. In this case, the cost (the result of waiting for the outcome) is higher if the true hypothesis is more time-sensitive. For example, if the true hypothesis is toxic chemical exposure (as opposed to a chronic disease such as diabetes), a delay of a few minutes could significantly increase the patient's risk of mortality. We propose a group greedy algorithm to solve this problem. We demonstrate that under worst-case scenarios, our algorithm has an approximation ratio of <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>. Importantly, when <span><math><mi>m</mi><mo>=</mo><mn>1</mn></math></span>, meaning there is only one group of hypotheses, our result is consistent with the logarithmic approximation bound for the traditional optimal decision tree problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114896"},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434047","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":"Algorithms for the thief orienteering problem on directed acyclic graphs","authors":"Andrew Bloch-Hansen ,&nbsp;Roberto Solis-Oba ,&nbsp;Daniel R. Page","doi":"10.1016/j.tcs.2024.114900","DOIUrl":"10.1016/j.tcs.2024.114900","url":null,"abstract":"<div><div>We consider the scenario of routing an agent called a <em>thief</em> through a weighted graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> from a start vertex <em>s</em> to an end vertex <em>t</em>. A set <em>I</em> of items each with weight <span><math><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and profit <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is distributed among <span><math><mi>V</mi><mo>∖</mo><mo>{</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>}</mo></math></span>. The thief, who has a knapsack of capacity <em>W</em>, must follow a simple path from <em>s</em> to <em>t</em> within a given time <em>T</em> while packing in the knapsack a set of items taken from the vertices along the path of total weight at most <em>W</em> and maximum profit. The travel time across an edge depends on the edge length and current knapsack load.</div><div>The thief orienteering problem (ThOP) is a generalization of the orienteering problem, the longest path problem, and the 0-1 knapsack problem. We prove that there exists no approximation algorithm for ThOP with constant approximation ratio unless <span><math><mtext>P</mtext><mo>=</mo><mtext>NP</mtext></math></span>, and we present a polynomial-time approximation scheme (PTAS) for a relaxed version of ThOP when <em>G</em> is directed and acyclic that produces solutions that use time at most <span><math><mi>T</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></math></span> for any constant <span><math><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></math></span>. We also present a fully polynomial-time approximation scheme (FPTAS) for ThOP on arbitrary undirected graphs where the travel time depends only on the lengths of the edges and <em>T</em> is the length of a shortest path from <em>s</em> to <em>t</em> plus a constant <em>K</em>. Finally, we present a FPTAS for a restricted version of the problem where the input graph is a clique.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114900"},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427852","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":"Verifiable attribute-based multi-keyword search scheme with sensitive information hiding for cloud-assisted e-healthcare sharing systems","authors":"Jie Zhao ,&nbsp;Hejiao Huang ,&nbsp;Yongliang Xu ,&nbsp;Xiaojun Zhang ,&nbsp;Hongwei Du ,&nbsp;Chao Huang","doi":"10.1016/j.tcs.2024.114895","DOIUrl":"10.1016/j.tcs.2024.114895","url":null,"abstract":"<div><div>Cloud-assisted e-healthcare sharing systems (EHSSs) play an increasingly pivotal role in the contemporary healthcare field. By outsourcing electronic medical records (EMRs) to the cloud, hospitals can alleviate local storage and management burdens while facilitating data sharing. Due to the highly sensitive nature of EMRs, encryption is necessary before storing them on the cloud. Attribute-based keyword search (ABKS) enables the privacy protection of EMRs with efficient search services. However, there remain some limitations in practical application. Firstly, most ABKS schemes only support single keyword queries, resulting in inaccurate results and wastage of computing and bandwidth resources. Secondly, since sensitive information within EMRs is encrypted as a whole, different data users (including internal doctors and external researchers) should have varying access rights to prevent leakage of this sensitive information. Thirdly, incorrect search results could lead to misdiagnosis or endanger patients' lives and affect researchers' decision-making processes. To effectively tackle these challenges, this paper proposes a verifiable attribute-based multi-keyword search scheme with sensitive information hiding (VABMKS-SIH) for cloud-assisted EHSSs, where we present a secure model for multi-keyword search with two-level access structure by incorporating an improved blindness filtering technique into ciphertext-policy attribute-based encryption (CP-ABE) within existing keyword search framework. Our scheme employs a super-increasing sequence to aggregate multiple filtered data blocks into one unified ciphertext, thereby greatly reducing communication overhead during the transmission phases of ciphertext. To check the correctness of returned results, we introduce a lightweight algebraic signature algorithm based on fundamental algebraic operations. A security analysis demonstrates that VABMKS-SIH is provably secure under the random oracle mode. Additionally, we also evaluate the proposed scheme's performance to demonstrate its utility in cloud-assisted EHSSs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114895"},"PeriodicalIF":0.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427853","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}