The Complexity of Social Coordination

Coordination is a challenging everyday task; just think of the last time you organized a party or a meeting involving several people. As a growing part of our social and professional life goes online, an opportunity for an improved coordination process arises. Recently, Gupta et al. proposed entangled queries as a declarative abstraction for data-driven coordination, where the difficulty of the coordination task is shifted from the user to the database. Unfortunately, evaluating entangled queries is very hard, and thus previous work considered only a restricted class of queries that satisfy safety (the coordination partners are fixed) and uniqueness (all queries need to be satisfied). In this paper we significantly extend the class of feasible entangled queries beyond uniqueness and safety. First, we show that we can simply drop uniqueness and still efficiently evaluate a set of safe entangled queries. Second, we show that as long as all users coordinate on the same set of attributes, we can give an efficient algorithm for coordination even if the set of queries does not satisfy safety. In an experimental evaluation we show that our algorithms are feasible for a wide spectrum of coordination scenarios.

💡 Research Summary

This paper, titled “The Complexity of Social Coordination,” presents significant advancements in evaluating “entangled queries,” a declarative abstraction for data-driven coordination that shifts the burden of coordinating activities (like planning meetings or group travel) from users to a database system.

The core challenge lies in finding a “coordinating set”—a subset of entangled queries that can be mutually satisfied, where each query’s postconditions (specifying coordination partners) are fulfilled by other queries’ head atoms. Prior work by Gupta et al. established that evaluating general entangled queries is intractable and thus focused only on queries satisfying two strict properties: safety (each user’s coordination target is uniquely identifiable) and uniqueness (all queries are interdependent, forming a single connected component in the coordination graph).

This work makes three key contributions to substantially broaden the class of feasible coordination scenarios. First, it provides a clear complexity separation, proving that finding a coordinating set is NP-hard even for databases with just two domain values, highlighting that the hardness stems from the relational dependencies between queries, not from standard database query evaluation.

Second, it introduces an efficient algorithm that eliminates the uniqueness requirement while maintaining the safety property. The algorithm identifies Strongly Connected Components (SCCs) in the coordination graph of safe queries. It then treats each SCC as an atomic unit, issuing a single combined database query to check if all queries within an SCC can be satisfied simultaneously. This guarantees finding a coordinating set if one exists, though finding the maximum such set remains NP-hard.

Third, and most practically, it proposes an efficient algorithm that drops both the uniqueness and safety requirements for a large class of natural scenarios. It focuses on applications where all users coordinate on the same set of attributes (e.g., destination and date for a trip). The algorithm enumerates possible values for these common coordination attributes (e.g., each concert venue on a tour). For each candidate value, it constructs a potential coordinating set comprising users who either specified that value or placed no restriction on it. It then filters this set by verifying each user’s remaining, non-coordination conditions (e.g., flight availability). This approach successfully handles unsafe queries where users specify types of partners (e.g., “any friend”) rather than specific individuals. The paper also shows a sharp complexity boundary: adding just one extra coordination attribute for a subset of users makes the problem intractable again.

Finally, the paper supports its theoretical contributions with a thorough experimental evaluation, demonstrating that the proposed algorithms are efficient and practical for a wide spectrum of real-world coordination problems, significantly extending the frontier of feasible data-driven coordination.