Social coordination allows users to move beyond awareness of their friends to efficiently coordinating physical activities with others. While specific forms of social coordination can be seen in tools such as Evite, Meetup and Groupon, we introduce a more general model using what we call enmeshed queries. An enmeshed query allows users to declaratively specify an intent to coordinate by specifying social attributes such as the desired group size and who what when, and the database returns matching queries. Enmeshed queries are continuous, but new queries (and not data) answer older queries; the variable group size also makes enmeshed queries different from entangled queries, publish-subscribe systems, and dating services. We show that even offline group coordination using enmeshed queries is NP-hard. We then introduce efficient heuristics that use selective indices such as location and time to reduce the space of possible matches; we also add refinements such as delayed evaluation and using the relative matchability of users to determine search order. We describe a centralized implementation and evaluate its performance against an optimal algorithm. We show that the combination of not stopping prematurely (after finding a match) and delayed evaluation results in an algorithm that finds 86 of the matches found by an optimal algorithm, and takes an average of 40 usec per query using 1 core of a 2.5 Ghz server machine. Further, the algorithm has good latency, is reasonably fair to large group size requests, and can be scaled to global workloads using multiple cores and multiple servers. We conclude by describing potential generalizations that add prices, recommendations, and data mining to basic enmeshed queries.
There is also related work on team formation in social networks @cite_2 that studies the following problem: given a set of people (i.e. nodes in a graph) with certain skills and communication costs across people (i.e. edges in the graph), and a task @math that requires some set of skills, find a subset of people to perform @math with minimal communication costs. They prove that such problems are NP hard, and describe heuristics to reduce computation. Our problem is not the same as task formation because tasks are not explicit first-class entities in enmeshed queries but are, instead, implicit in the desires of users. Further, our metric is maximizing matches and not minimizing communication.
@cite_2
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Given a task T, a pool of individuals X with different skills, and a social network G that captures the compatibility among these individuals, we study the problem of finding X, a subset of X, to perform the task. We call this the T EAM F ORMATION problem. We require that members of X' not only meet the skill requirements of the task, but can also work effectively together as a team. We measure effectiveness using the communication cost incurred by the subgraph in G that only involves X'. We study two variants of the problem for two different communication-cost functions, and show that both variants are NP-hard. We explore their connections with existing combinatorial problems and give novel algorithms for their solution. To the best of our knowledge, this is the first work to consider the T EAM F ORMATION problem in the presence of a social network of individuals. Experiments on the DBLP dataset show that our framework works well in practice and gives useful and intuitive results. We consider estimation of worker skills from worker-task interaction data (with unknown labels) for the single-coin crowd-sourcing binary classification model in symmetric noise. We define the (worker) interaction graph whose nodes are workers and an edge between two nodes indicates whether or not the two workers participated in a common task. We show that skills are asymptotically identifiable if and only if an appropriate limiting version of the interaction graph is irreducible and has odd-cycles. We then formulate a weighted rank-one optimization problem to estimate skills based on observations on an irreducible, aperiodic interaction graph. We propose a gradient descent scheme and show that for such interaction graphs estimates converge asymptotically to the global minimum. We characterize noise robustness of the gradient scheme in terms of spectral properties of signless Laplacians of the interaction graph. We then demonstrate that a plug-in estimator based on the estimated skills achieves state-of-art performance on a number of real-world datasets. Our results have implications for rank-one matrix completion problem in that gradient descent can provably recover @math rank-one matrices based on @math off-diagonal observations of a connected graph with a single odd-cycle. We study the complexity of motivating time-inconsistent agents to complete long term projects in a graph-based planning model as proposed by Kleinberg and Oreni¾?[5]. Given a task graph G with n nodes, our objective is to guide an agent towards a target node t under certain budget constraints. The crux is that the agent may change its strategy over time due to its present-bias. We consider two strategies to guide the agent. First, a single reward is placed at t and arbitrary edges can be removed from G. Secondly, rewards can be placed at arbitrary nodes of G but no edges must be deleted. In both cases we show that it is NP-complete to decide if a given budget is sufficient to guide the agent. For the first setting, we give complementing upper and lower bounds on the approximability of the minimum required budget. In particular, we devise a @math 1+n-approximation algorithm and prove NP-hardness for ratios greater than @math n 3. Finally, we argue that the second setting does not permit any efficient approximation unless @math P=NP. Let a communication network be modelled by a directed graphG = (V,E) of n nodes and m edges. We consider aone-round two-player network pricing game, the Stackelberg ShortestPaths Tree (StackSPT) game. This is played on G, by assuming thatedges in E are partitioned into two sets: a set E F of edges with afixed positive real weight, and a set E P of edges that should bepriced by one of the two players (the leader). Given adistinguished node r ∈ V, the StackSPT game isthen as follows: the leader prices the edges in E P in such a waythat he will maximize his revenue, knowing that the other player(the follower) will build a shortest paths tree of G rooted at r,say S(r), by running a publicly available algorithm. Quitenaturally, for each edge selected in the solution, theleader’s revenue is assumed to be equal to the loaded priceof an edge, namely the product of the edge price times the numberof paths from r in S(r) that use it. First, we show that theproblem of maximizing the leader’s revenue is NP-hard as soonas |E P | = Θ(n). Then, in search of aneffective method for solving the problem when the size of E P isconstant, we focus on the basic case in which |E P| = 2, and we provide an efficient O(n 2 logn) timealgorithm. Afterwards, we generalize the approach to the case |E P| = k, and we show that it can be solved inpolynomial time whenever k = O(1).