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Pebble guided Treasure Hunt in Plane 鹅卵石引导寻宝在飞机上
Adri Bhattacharya, B. Gorain, P. Mandal
We study the problem of treasure hunt in a Euclidean plane by a mobile agent with the guidance of pebbles. The initial position of the agent and position of the treasure are modeled as special points in the Euclidean plane. The treasure is situated at a distance at most $D>0$ from the initial position of the agent. The agent has a perfect compass, but an adversary controls the speed of the agent. Hence, the agent can not measure how much distance it traveled for a given time. The agent can find the treasure only when it reaches the exact position of the treasure. The cost of the treasure hunt is defined as the total distance traveled by the agent before it finds the treasure. The agent has no prior knowledge of the position of the treasure or the value of $D$. An Oracle, which knows the treasure's position and the agent's initial location, places some pebbles to guide the agent towards the treasure. Once decided to move along some specified angular direction, the agent can decide to change its direction only when it encounters a pebble or a special point. We ask the following central question in this paper: ``For given $k ge 0$, What is cheapest treasure hunt algorithm if at most $k$ pebbles are placed by the Oracle?"We show that for $k=1$, there does not exist any treasure hunt algorithm that finds the treasure with finite cost. We show the existence of an algorithm with cost $O(D)$ for $k=2$. For $k>8$ we have designed an algorithm that uses $k$ many pebbles to find the treasure with cost $O(k^{2}) + D(sintheta' + costheta')$, where $theta'=frac{pi}{2^{k-8}}$. The second result shows the existence of an algorithm with cost arbitrarily close to $D$ for sufficiently large values of $D$.
研究了一个移动智能体在欧氏平面上的寻宝问题。代理人的初始位置和宝藏的位置被建模为欧几里得平面上的特殊点。宝藏位于离代理人初始位置最多$D>0$的距离。代理人有一个完美的指南针,但对手控制代理人的速度。因此,智能体无法测量在给定时间内移动了多少距离。代理商只有在到达宝藏的确切位置时才能找到宝藏。寻宝的成本定义为agent在找到宝藏之前走过的总距离。代理人事先不知道宝藏的位置或$D$的价值。一个知道宝藏的位置和代理的初始位置的神谕,放置一些鹅卵石来引导代理走向宝藏。一旦决定沿着某个指定的角度方向移动,代理只能在遇到鹅卵石或特殊点时决定改变其方向。我们在本文中提出以下中心问题:对于给定$k ge 0$,如果Oracle最多放置$k$个鹅卵石,那么最便宜的寻宝算法是什么?“我们表明,对于$k=1$,不存在任何以有限成本找到宝藏的寻宝算法。我们证明了对$k=2$的代价为$O(D)$的算法的存在性。对于$k>8$,我们设计了一个算法,使用$k$许多鹅卵石找到宝藏,成本为$O(k^{2}) + D(sintheta' + costheta')$,其中$theta'=frac{pi}{2^{k-8}}$。第二个结果表明,对于足够大的$D$值,存在一个代价任意接近$D$的算法。
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引用次数: 0
Consensus on an Unknown Torus with Dense Byzantine Faults 一个具有密集拜占庭断层的未知环面的共识
Joseph Oglio, Kendric Hood, Gokarna Sharma, Mikhail Nesterenko
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引用次数: 0
Distance-2-Dispersion: Dispersion with Further Constraints 距离-2-分散:具有进一步约束的分散
Tanvir Kaur, Kaushik Mondal
The aim of the dispersion problem is to place a set of $k(leq n)$ mobile robots in the nodes of an unknown graph consisting of $n$ nodes such that in the final configuration each node contains at most one robot, starting from any arbitrary initial configuration of the robots on the graph. In this work we propose a variant of the dispersion problem where we start with any number of robots, and put an additional constraint that no two adjacent nodes contain robots in the final configuration. We name this problem as Distance-2-Dispersion (D-2-D). However, even if the number of robots $k$ is less than $n$, it may not possible for each robot to find a distinct node to reside, maintaining our added constraint. Specifically, if a maximal independent set is already formed by the nodes which contain a robot each, then other robots, if any, who are searching for a node to seat, will not find one. Hence we allow multiple robots to seat on some nodes only if there is no place to seat. If $kgeq n$, it is guaranteed that the nodes with robots form a maximal independent set of the underlying network. The graph $G=(V, E)$ has $n$ nodes and $m$ edges, where nodes are anonymous. It is a port labelled graph, i.e., each node $u$ assigns a distinct port number to each of its incident edges from a range $[0,delta-1]$ where $delta$ is the degree of the node $u$. The robots have unique ids in the range $[1, L]$, where $L ge k$. Co-located robots can communicate among themselves. We provide an algorithm that solves D-2-D starting from a rooted configuration (i.e., initially all the robots are co-located) and terminate after $2Delta(8m-3n+3)$ synchronous rounds using $O(log Delta)$ memory per robot without using any global knowledge of the graph parameters $m$, $n$ and $Delta$, the maximum degree of the graph. We also provide $Omega(mDelta)$ lower bound on the number of rounds for the D-2-D problem.
分散问题的目的是将一组$k(leq n)$移动机器人放置在由$n$节点组成的未知图的节点中,使得在最终配置中每个节点最多包含一个机器人,从图上机器人的任意初始配置开始。在这项工作中,我们提出了分散问题的一个变体,我们从任意数量的机器人开始,并添加了一个额外的约束,即在最终配置中没有两个相邻节点包含机器人。我们把这个问题称为距离-2-离散(D-2-D)。然而,即使机器人的数量$k$小于$n$,每个机器人也不可能找到一个不同的节点驻留,从而维持我们添加的约束。具体来说,如果每个节点都包含一个机器人的节点已经形成了一个最大独立集,那么其他机器人(如果有的话)正在寻找一个节点来安置,将不会找到一个。因此,我们允许多个机器人仅在没有位置可坐的情况下坐在某些节点上。如果$kgeq n$,则保证具有机器人的节点构成底层网络的最大独立集。图$G=(V, E)$有$n$个节点和$m$条边,其中的节点是匿名的。它是一个端口标记图,即,每个节点$u$从一个范围$[0,delta-1]$ ($delta$是节点的度数$u$)为其每个事件边分配一个不同的端口号。机器人的id范围是$[1, L]$,其中$L ge k$。位于同一位置的机器人可以相互通信。我们提供了一种算法,该算法从根配置(即,最初所有机器人都位于同一位置)开始解决D-2-D问题,并在使用每个机器人$O(log Delta)$内存的$2Delta(8m-3n+3)$同步轮之后终止,而不使用图参数$m$, $n$和$Delta$(图的最大程度)的任何全局知识。我们还提供了D-2-D问题的轮数的$Omega(mDelta)$下界。
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引用次数: 2
Case Study on the Performance of ML-Based Network Intrusion Detection Systems in SDN 基于机器学习的SDN网络入侵检测系统性能的实例研究
Adnane Mzibri, R. Benaini, M. B. Mamoun
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引用次数: 0
Comparing Causal Convergence Consistency Models 比较因果收敛一致性模型
Sidi Mohamed Beillahi, A. Bouajjani, C. Enea
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引用次数: 0
Edge-Based Bird Species Recognition via Active Learning 基于主动学习的边缘鸟类物种识别
Hicham Bellafkir, M. Vogelbacher, Daniel Schneider, M. Mühling, Nikolaus Korfhage, Bernd Freisleben
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引用次数: 0
A Peer to Peer Federated Graph Neural Network for Threat Intelligence 面向威胁情报的点对点联邦图神经网络
Mouad Bouharoun, Bilal Taghdouti, M. Erradi
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引用次数: 0
A Formal Analysis of Karn's Algorithm Karn算法的形式分析
Max von Hippel, K. McMillan, C. Nita-Rotaru, L. Zuck
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引用次数: 2
Detection of Fake News Through Heterogeneous Graph Interactions 基于异构图交互的假新闻检测
Raed Alharbi, Tre' R. Jeter, M. Thai
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引用次数: 0
Beyond Locks and Keys: Structural Equation Modeling Based Framework to Explore Security Breaches Through the Lens of Crime Theories 超越锁和钥匙:基于结构方程模型的框架,通过犯罪理论的镜头探索安全漏洞
Narjisse Nejjari, Karim Zkik, H. Benbrahim, Mounir Ghogho
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引用次数: 0
期刊
Proceedings of the ... International Conference on Embedded Networked Sensor Systems. International Conference on Embedded Networked Sensor Systems
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