In this paper, we investigate recommender systems from a network perspective and investigate recommendation networks, where nodes are items (e.g., movies) and edges are constructed from top-N recommendations (e.g., related movies). In particular, we focus on evaluating the reachability and navigability of recommendation networks and investigate the following questions: (i) How well do recommendation networks support navigation and exploratory search? (ii) What is the influence of parameters, in particular different recommendation algorithms and the number of recommendations shown, on reachability and navigability? and (iii) How can reachability and navigability be improved in these networks? We tackle these questions by first evaluating the reachability of recommendation networks by investigating their structural properties. Second, we evaluate navigability by simulating three different models of information seeking scenarios. We find that with standard algorithms, recommender systems are not well suited to navigation and exploration and propose methods to modify recommendations to improve this. Our work extends from one-click-based evaluations of recommender systems towards multi-click analysis (i.e., sequences of dependent clicks) and presents a general, comprehensive approach to evaluating navigability of arbitrary recommendation networks.
Kleinberg also found that an network possesses certain structural properties that make it possible to design efficient local search algorithms (i.e., algorithms that only have local knowledge of the network) @cite_22 @cite_28 . The delivery time (the expected number of steps to reach an arbitrary target node) of such algorithms is then sub-linear in @math . In this paper, we investigate the efficient navigability of networks through the simulation of a range of search and navigation models.
@cite_28 @cite_22
2589022566 2087097376 2293971114 2950657833
We consider a system, comprising a library of @math files (e.g., movies) and a wireless network with a @math transmitters, each equipped with a local cache of size of @math files and a @math receivers, each equipped with a local cache of size of @math files. Each receiver will ask for one of the @math files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers’ future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of @math is achievable, and this is within a factor of 2 of the optimum, under uncoded prefetching and one-shot linear delivery schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes ), (ii) the transmitters’ caches and receivers’ caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network. To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitter’s caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receiver’s caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF. Consider a team of mobile software agents deployed to capture a (possibly hostile) intruder in a network. All agents, including the intruder move along the network links; the intruder could be arbitrarily fast, and aware of the positions of all the agents. The problem is to design the agents' strategy for capturing the intruder. The main efficiency parameter is the size of the team. This is an instance of the well known graph-searching problem whose many variants have been extensively studied in the literature. In all existing solutions, and in all the variants of the problem, it is assumed that agents can be removed from their current location and placed in another network site arbitrarily and at any time. As a consequence, the existing optimal strategies cannot be employed in situations for which agents cannot access the network at any point, or cannot "jump" across the network, or cannot reach an arbitrary point of the network via an internal travel through insecure zones. This motivates the contiguous search problem in which agents cannot be removed from the network, and clear links must form a connected sub-network at any time, providing safety of movements. This new problem is NP-complete in general. We study it for tree networks, and we consider its more general version, the weighted case, which arises naturally when considering networks whose nodes and links are of different nature and thus require a different number of agents to be explored. We give a linear-time algorithm that computes, for any tree @math , the minimum number of agents to capture the intruder, and the corresponding search strategy. Beside its optimality in time, our algorithm is naturally distributed: if @math is a processor-network, then the minimal search strategy for @math can be computed by @math in a decentralized manner, using a linear number of messages. Given a network represented by a graph @math G=V,E, we consider a dynamical process of influence diffusion in G that evolves as follows: Initially only the nodes of a given @math S⊆V are influenced; subsequently, at each round, the set of influenced nodes is augmented by all the nodes in the network that have a sufficiently large number of already influenced neighbors. The question is to determine a small subset of nodes Sa target set that can influence the whole network. This is a widely studied problem that abstracts many phenomena in the social, economic, biological, and physical sciences. It is known [6] that the above optimization problem is hard to approximate within a factor of @math 2log1-∈|V|, for any @math ∈>0. In this paper, we present a fast and surprisingly simple algorithm that exhibits the following features: 1 when applied to trees, cycles, or complete graphs, it always produces an optimal solution i.e., a minimum size target set; 2 when applied to arbitrary networks, it always produces a solution of cardinality matching the upper bound given in [1], and proved therein by means of the probabilistic method; 3 when applied to real-life networks, it always produces solutions that substantially outperform the ones obtained by previously published algorithms for which no proof of optimality or performance guarantee is known in any class of graphs. We study the power of for optimization problems on social networks. We focus on sequential algorithms for which the network topology is initially unknown and is revealed only within a local neighborhood of vertices that have been irrevocably added to the output set. The distinguishing feature of this setting is that locality is necessitated by constraints on the network information visible to the algorithm, rather than being desirable for reasons of efficiency or parallelizability. In this sense, changes to the level of network visibility can have a significant impact on algorithm design. We study a range of problems under this model of algorithms with local information. We first consider the case in which the underlying graph is a preferential attachment network. We show that one can find the node of maximum degree in the network in a polylogarithmic number of steps, using an opportunistic algorithm that repeatedly queries the visible node of maximum degree. This addresses an open question of Bollob 'a s and Riordan. In contrast, local information algorithms require a linear number of queries to solve the problem on arbitrary networks. Motivated by problems faced by recruiters in online networks, we also consider network coverage problems such as finding a minimum dominating set. For this optimization problem we show that, if each node added to the output set reveals sufficient information about the set's neighborhood, then it is possible to design randomized algorithms for general networks that nearly match the best approximations possible even with full access to the graph structure. We show that this level of visibility is necessary. We conclude that a network provider's decision of how much structure to make visible to its users can have a significant effect on a user's ability to interact strategically with the network.