1,199 research outputs found

    Edge Contraction and Line Graphs

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    Given a family of graphs H\mathcal{H}, a graph GG is H\mathcal{H}-free if any subset of V(G)V(G) does not induce a subgraph of GG that is isomorphic to any graph in H\mathcal{H}. We present sufficient and necessary conditions for a graph GG such that G/eG/e is H\mathcal{H}-free for any edge ee in E(G)E(G). Thereafter, we use these conditions to characterize claw-free and line graphs.Comment: arXiv admin note: text overlap with arXiv:2203.0349

    On Cops and Robbers on GΞG^{\Xi} and cop-edge critical graphs

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    Cop Robber game is a two player game played on an undirected graph. In this game cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. In this paper we presents results concerning games on GΞG^{\Xi}, that is the graph obtained by connecting the corresponding vertices in GG and its complement G‾\overline{G}. In particular we show that for planar graphs c(GΞ)≤3c(G^{\Xi})\leq 3. Furthermore we investigate the cop-edge critical graphs, i.e. graphs that for any edge ee in GG we have either c(G−e)c(G)c(G-e)c(G). We show couple examples of cop-edge critical graphs having cop number equal to 33

    Contributions to Edge Computing

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    Efforts related to Internet of Things (IoT), Cyber-Physical Systems (CPS), Machine to Machine (M2M) technologies, Industrial Internet, and Smart Cities aim to improve society through the coordination of distributed devices and analysis of resulting data. By the year 2020 there will be an estimated 50 billion network connected devices globally and 43 trillion gigabytes of electronic data. Current practices of moving data directly from end-devices to remote and potentially distant cloud computing services will not be sufficient to manage future device and data growth. Edge Computing is the migration of computational functionality to sources of data generation. The importance of edge computing increases with the size and complexity of devices and resulting data. In addition, the coordination of global edge-to-edge communications, shared resources, high-level application scheduling, monitoring, measurement, and Quality of Service (QoS) enforcement will be critical to address the rapid growth of connected devices and associated data. We present a new distributed agent-based framework designed to address the challenges of edge computing. This actor-model framework implementation is designed to manage large numbers of geographically distributed services, comprised from heterogeneous resources and communication protocols, in support of low-latency real-time streaming applications. As part of this framework, an application description language was developed and implemented. Using the application description language a number of high-order management modules were implemented including solutions for resource and workload comparison, performance observation, scheduling, and provisioning. A number of hypothetical and real-world use cases are described to support the framework implementation

    Geometric Pursuit Evasion

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    In this dissertation we investigate pursuit evasion problems set in geometric environments. These games model a variety of adversarial situations in which a team of agents, called pursuers, attempts to catch a rogue agent, called the evader. In particular, we consider the following problem: how many pursuers, each with the same maximum speed as the evader, are needed to guarantee a successful capture? Our primary focus is to provide combinatorial bounds on the number of pursuers that are necessary and sufficient to guarantee capture. The first problem we consider consists of an unpredictable evader that is free to move around a polygonal environment of arbitrary complexity. We assume that the pursuers have complete knowledge of the evader's location at all times, possibly obtained through a network of cameras placed in the environment. We show that regardless of the number of vertices and obstacles in the polygonal environment, three pursuers are always sufficient and sometimes necessary to capture the evader. We then consider several extensions of this problem to more complex environments. In particular, suppose the players move on the surface of a 3-dimensional polyhedral body; how many pursuers are required to capture the evader? We show that 4 pursuers always suffice (upper bound), and that 3 are sometimes necessary (lower bound), for any polyhedral surface with genus zero. Generalizing this bound to surfaces of genus g, we prove the sufficiency of (4g + 4) pursuers. Finally, we show that 4 pursuers also suffice under the "weighted region" constraints, where the movement costs through different regions of the (genus zero) surface have (different) multiplicative weights. Next we consider a more general problem with a less restrictive sensing model. The pursuers' sensors are visibility based, only providing the location of the evader if it is in direct line of sight. We begin my making only the minimalist assumption that pursuers and the evader have the same maximum speed. When the environment is a simply-connected (hole-free) polygon of n vertices, we show that Θ(n^1/2 ) pursuers are both necessary and sufficient in the worst-case. When the environment is a polygon with holes, we prove a lower bound of Ω(n^2/3 ) and an upper bound of O(n^5/6 ) pursuers, where n includes the vertices of the hole boundaries. However, we show that with realistic constraints on the polygonal environment these bounds can be drastically improved. Namely, if the players' movement speed is small compared to the features of the environment, we give an algorithm with a worst case upper bound of O(log n) pursuers for simply-connected n-gons and O(√h + log n) for polygons with h holes. The final problem we consider takes a small step toward addressing the fact that location sensing is noisy and imprecise in practice. Suppose a tracking agent wants to follow a moving target in the two-dimensional plane. We investigate what is the tracker's best strategy to follow the target and at what rate does the distance between the tracker and target grow under worst-case localization noise. We adopt a simple but realistic model of relative error in sensing noise: the localization error is proportional to the true distance between the tracker and the target. Under this model we are able to give tight upper and lower bounds for the worst-case tracking performance, both with or without obstacles in the Euclidean plane

    Spartan Daily, October 18, 2005

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    Volume 125, Issue 30https://scholarworks.sjsu.edu/spartandaily/10173/thumbnail.jp

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    35th Symposium on Theoretical Aspects of Computer Science: STACS 2018, February 28-March 3, 2018, Caen, France

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