Robotic swarms are decentralized multi-robot systems whose members use local information from proximal neighbors to execute simple reactive control laws that result in emergent collective behaviors. In contrast, members of a general multi-robot system may have access to global information, allto-all communication or sophisticated deliberative collaboration. Some algorithms in the literature are applicable to robotic swarms. Others require the extra complexity of general multirobot systems. Given an application domain, a system designer or supervisory operator must choose an appropriate system or algorithm respectively that will enable them to achieve their goals while satisfying mission constraints (e.g. bandwidth, energy, time limits). In this paper, we compare representative swarm and general multi-robot algorithms in two application domains -navigation and dynamic area coverage -with respect to several metrics (e.g. completion time, distance travelled). Our objective is to characterize each class of algorithms to inform offline system design decisions by engineers or online algorithm selection decisions by supervisory operators. Our contributions are (a) an empirical performance comparison of representative swarm and general multi-robot algorithms in two application domains, (b) a comparative analysis of the algorithms based on the theory of information invariants, which provides a theoretical characterization supported by our empirical results.

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We study the problem of assortative and disassortative partitions on random d-regular graphs. Nodes in the graph are partitioned into two non-empty groups. In the assortative partition every node requires at least H of their neighbors to be in their own group. In the disassortative partition they require less than H neighbors to be in their own group. Using the cavity method based on analysis of the Belief Propagation algorithm we establish for which combinations of parameters (d,H) these partitions exist with high probability and for which they do not. For H>⌈d/2⌉ we establish that the structure of solutions to the assortative partition problems corresponds to the so-called frozen-1RSB. This entails a conjecture of algorithmic hardness of finding these partitions efficiently. For H≤⌈d/2⌉ we argue that the assortative partition problem is algorithmically easy on average for all d. Further we provide arguments about asymptotic equivalence between the assortative partition problem and the disassortative one, going trough a close relation to the problem of single-spin-flip-stable states in spin glasses. In the context of spin glasses, our results on algorithmic hardness imply a conjecture that gapped single spin flip stable states are hard to find which may be a universal reason behind the observation that physical dynamics in glassy systems display convergence to marginal stability.