联合资源博弈问题的参数化复杂性

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摘要翻译：
联盟形成是多Agent系统中的一个关键问题。联盟使代理人能够实现他们自己可能无法实现的目标。以前的工作表明，联盟游戏中的问题在计算上是困难的。Wooldridge和Dunne(Altional Intelligence，2006)研究了资源联盟博弈(CRG)中几个自然决策问题的经典计算复杂性。在CRG博弈中，每个agent被赋予一组资源，如果它们被共同赋予必要数量的资源，联盟可以实现一组目标。联盟资源博弈的输入将agent集Ag、目标集G、资源集R等几个要素捆绑在一起。Shrot、Aumann和Kraus(AAMAS2009)利用参数化复杂性理论研究了CRG模型中的联盟形成问题。他们精炼的分析表明，并不是所有输入部分的作用都是平等的--问题的一些例子确实是容易处理的，而另一些仍然是难以处理的。我们回答了Shrot、Aumann和Kraus留下的一个重要问题，证明了SC问题（检验一个联盟是否成功）在用联盟规模参数化时是W[1]-难的。然后通过一个从SC出发的约简主题，我们可以证明Wooldridge等人引入的与资源、资源边界和资源冲突有关的各种问题是1。w[1]-硬或co-w[1]-硬，当由联盟的大小参数化时。2.用R3参数化时的para-NP-hard或co-para-NP-hard。用G或Ag+R参数化时的FPT。
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英文标题：
《Parameterized Complexity of Problems in Coalitional Resource Games》
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作者：
Rajesh Chitnis, MohammadTaghi Hajiaghayi, Vahid Liaghat
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最新提交年份：
2011
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Computational Complexity        计算复杂度
分类描述：Covers models of computation, complexity classes, structural complexity, complexity tradeoffs, upper and lower bounds. Roughly includes material in ACM Subject Classes F.1 (computation by abstract devices), F.2.3 (tradeoffs among complexity measures), and F.4.3 (formal languages), although some material in formal languages may be more appropriate for Logic in Computer Science. Some material in F.2.1 and F.2.2, may also be appropriate here, but is more likely to have Data Structures and Algorithms as the primary subject area.
涵盖计算模型，复杂度类别，结构复杂度，复杂度折衷，上限和下限。大致包括ACM学科类F.1（抽象设备的计算）、F.2.3（复杂性度量之间的权衡）和F.4.3（形式语言）中的材料，尽管形式语言中的一些材料可能更适合于计算机科学中的逻辑。在F.2.1和F.2.2中的一些材料可能也适用于这里，但更有可能以数据结构和算法作为主要主题领域。
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一级分类：Computer Science        计算机科学
二级分类：Computer Science and Game Theory        计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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英文摘要：
  Coalition formation is a key topic in multi-agent systems. Coalitions enable agents to achieve goals that they may not have been able to achieve on their own. Previous work has shown problems in coalitional games to be computationally hard. Wooldridge and Dunne (Artificial Intelligence 2006) studied the classical computational complexity of several natural decision problems in Coalitional Resource Games (CRG) - games in which each agent is endowed with a set of resources and coalitions can bring about a set of goals if they are collectively endowed with the necessary amount of resources. The input of coalitional resource games bundles together several elements, e.g., the agent set Ag, the goal set G, the resource set R, etc. Shrot, Aumann and Kraus (AAMAS 2009) examine coalition formation problems in the CRG model using the theory of Parameterized Complexity. Their refined analysis shows that not all parts of input act equal - some instances of the problem are indeed tractable while others still remain intractable.   We answer an important question left open by Shrot, Aumann and Kraus by showing that the SC Problem (checking whether a Coalition is Successful) is W[1]-hard when parameterized by the size of the coalition. Then via a single theme of reduction from SC, we are able to show that various problems related to resources, resource bounds and resource conflicts introduced by Wooldridge et al are 1. W[1]-hard or co-W[1]-hard when parameterized by the size of the coalition. 2. para-NP-hard or co-para-NP-hard when parameterized by |R|. 3. FPT when parameterized by either |G| or |Ag|+|R|.
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PDF链接：
https://arxiv.org/pdf/1105.0707

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关键词：复杂性 Intelligence Coordination Presentation Applications 理论 para 输入 CRG 冲突