Abstract-In this paper, we consider the problem of assigning a set of clients with demands to a set of servers with capacities and degree constraints. The goal is to find an allocation such that the number of clients assigned to a server is smaller than the server's degree and their overall demand is smaller than the server's capacity, while maximizing the overall throughput. This problem has several natural applications in the context of independent tasks scheduling or virtual machines allocation. We consider both the offline (when clients are known beforehand) and the online (when clients can join and leave the system at any time) versions of the problem. We first show that the degree constraint on the maximal number of clients that a server can handle is realistic in many contexts. Then, our main contribution is to prove that even if it makes the allocation problem more difficult (NP-Complete), a very small additive resource augmentation on the servers degree is enough to find in polynomial time a solution that achieves at least the optimal throughput. After a set of theoretical results on the complexity of the offline and online versions of the problem, we propose several other greedy heuristics to solve the online problem and we compare the performance (in terms of throughput) and the cost (in terms of disconnections and reconnections) of proposed algorithms through a set of extensive simulation results.
Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.
The need for efficient decentralized recommender systems has been appreciated for some time, both for the intrinsic advantages of decentralization and the necessity of integrating recommender systems into P2P applications. On the other hand, the accuracy of recommender systems is often hurt by data sparsity. In this paper, we compare different decentralized user-based and item-based Collaborative Filtering (CF) algorithms with each other, and propose a new user-based random walk approach customized for decentralized systems, specifically designed to handle sparse data. We show how the application of random walks to decentralized environments is different from the centralized version. We examine the performance of our random walk approach in different settings by varying the sparsity, the similarity measure and the neighborhood size. In addition, we introduce the popularizing disadvantage of the significance weighting term traditionally used to increase the precision of similarity measures, and elaborate how it can affect the performance of the random walk algorithm. The simulations on MovieLens 10,000,000 ratings dataset demonstrate that over a wide range of sparsity, our algorithm outperforms other decentralized CF schemes. Moreover, our results show decentralized user-based approaches perform better than their item-based counterparts in P2P recommender applications.
Abstract. In this paper we start the study of generalizing the Adversarial Queueing Theory (aqt) model towards a continuous scenario in which the usually assumed synchronicity of the evolution is not required anymore. We consider a model, named continuous AQT (caqt), in which packets can have arbitrary lengths, and the network links may have different speeds (or bandwidths) and propagation delays. We show that, in such a general model, having bounded queues implies bounded endto-end packet delays and vice versa. From the network point of view, we show that networks with directed acyclic topologies are universally stable, i.e., stable independently of the protocols and the traffic patterns used in it, and that this even holds for traffic patterns that make links to be fully loaded. Concerning packet scheduling protocols, we show that the well-known lis, sis, ftg and nfs protocols remain universally stable in our model. We also show that the caqt model is strictly stronger than the aqt model by presenting scheduling policies that are unstable under the former while they are universally stable under the latter.
Abstract. Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs, recent empirical studies have proved that they fail to reflect some current practices in real social networks. In this paper we address the issue of drawing signed graphs and capturing such social interactions. We relax the previous assumptions to define a drawing as a model in which every vertex has to be placed closer to its neighbors connected through a positive edge than its neighbors connected through a negative edge in the resulting space. Based on this definition, we address the problem of deciding whether a given signed graph has a drawing in a givendimensional Euclidean space. We focus on the 1-dimensional case, where we provide a polynomial time algorithm that decides if a given complete signed graph has a drawing, and provides it when applicable.
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