A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989b) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin–Courant rule for preferences single-peaked on trees. We show that in this setting the egalitarian version of this rule admits a polynomial-time winner determination algorithm. For the utilitarian version, we prove that winner determination remains NP-hard for the Borda scoring function; indeed, this hardness results extends to a large family of scoring functions. However, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We then explore the power and limitations of this framework: we develop polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but show that it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.

In cloud computing environment, a larger number of tasks are executed simultaneously, and therefore task scheduling strategy is a key factor to determine the performance of the system. For the problem of static scheduling regarding related tasks in cloud environment, this paper minimizes the schedu ling length and keeps load balance as the main goal. By combining the list scheduling and task duplication algorithms, a new task scheduling algorithm is proposed. This algorithm is composed of three steps of operations. Firstly, a task scheduling queue is constructed by computing the priority value for each task; secondly, in order to reduce communication latency between tasks, the parent tasks of the current task are duplicated selectively by taking advantage of the timeslots of the current virtual machine rationally; lastly, each task is assigned to the virtual machine that made the task have the earliest execution time and keep load balanced of system. The experimental results display the influence of the number of tasks on the performance of the algorithm when CCR is different and the new task scheduling algorithm balances the loads among virtual machines in the cloud computing system, and improves the resource utilization effectively.

Summary With the development of Internet plus technologies such as IoT, cloud computing, mobile Internet, and big data analysis, several new forms of sports community, which provided significant conveniences to the exercisers, were proposed. However, online communications are still deficient, and relationships among exercisers and between exercisers and sports activities are absent. To solve these problems, an Internet plus O2O sports community was proposed, and the idea and methods of sports activities management are discussed in this paper. Firstly, the activity management framework contributed by activity organizers, participants, and followers is constructed using cloud storage technology. Responsibilities of different kinds of users and constitution of activity data are also described. Secondly, six personalized recommendation algorithms, including tag‐based, relationship‐based, ranking list–based, content‐based, content‐based collaborative filtering, and user‐based collaborative filtering algorithms and their application in sports community are presented. Thirdly, a novel activity management model is designed, which supports online‐offline deep fusion and provides management of the whole procedures of a sports activity. Primary tasks of different activity stages are described. Finally, analysis methods and exhibition forms of statistics, text, and multimedia data are discussed.

Algorithmic mechanism design is concerned with designing algorithms for settings where inputs are controlled by selfish agents, and the center needs to motivate the agents to report their true values. In this paper, we study scenarios where the center may be able to verify whether the agents report their preferences (types) truthfully. We first consider the standard model of mechanism design with partial verification, where the set of types that an agent can report is a function of his true type. We explore inherent limitations of this model; in particular, we show that the famous Gibbard--Satterthwaite impossibility result holds even if a manipulator can only lie by swapping two adjacent alternatives in his vote. Motivated by these negative results, we then introduce a richer model of verification, which we term mechanism design with probabilistic verification. In our model, an agent may report any type, but will be caught with some probability that may depend on his true type, the reported type, or both; if an agent is caught lying, he will not get his payment and may be fined. We characterize the class of social choice functions that can be truthfully implemented in this model. We then proceed to study the complexity of finding an optimal individually rational implementation, i.e., one that minimizes the center's expected payment while guaranteeing non-negative utility to the agent, both for truthful and for non-truthful implementation. Our hardness result for non-truthful implementation answers an open question recently posed by Auletta et al. [2011].

For low earth orbit satellite formation network, the performance of MAC depends on the degree of competition in the network. Contention-based MAC protocols such as CSMA suffer from inefficiency under the condition of high contention, but it is in the opposite way of slot-based MAC protocols such as TDMA performance. The mixed solution which combines both competition-based mechanism and schedule-based mechanism is important to resolve network effectivity. In this paper, we propose a LDMA (load-division multiple access) according to the characteristics of inter-satellite link in a small low orbit satellite formation network. Through experimental studies, we found that LDMA has the effective management for channel utilization both under the condition of low level competition and high level competition. And at the same time LDMA can effectively solve the problem of network congestion and transmission collision caused by the heavy load in the satellite formation network.

Slinko and White, (2008) have recently introduced a new model of coalitional manipulation of voting rules under limited communication, which they call safe strategic voting. The computational aspects of this model were first studied by Hazon and Elkind, (2010), who provide polynomial-time algorithms for finding a safe strategic vote under k-approval and the Bucklin rule. In this paper, we answer an open question of Hazon and Elkind, (2010) by presenting a polynomial-time algorithm for finding a safe strategic vote under the Borda rule. Our results for Borda generalize to several interesting classes of scoring rules.

Weak monotonicity is a simple necessary condition for a social choice function to be implementable by a truthful mechanism. Roberts [10] showed that it is sufficient for all social choice functions whose domain is unrestricted. Lavi, Mu'alem and Nisan [6] proved the sufficiency of weak monotonicity for functions over order-based domains and Gui, Muller and Vohra [5] proved sufficiency for order-based domains with range constraints and for domains defined by other special types of linear inequality constraints. Here we show the more general result, conjectured by Lavi, Mu'alem and Nisan [6], that weak monotonicity is sufficient for functions defined on any convex domain.