We propose a new class of algorithms for multirobot problems called “Any-Com”. With Any-Com, a suboptimal solution is found quickly and refined as communication permits (analogous to “Any-Time” where a suboptimal solution is refined as time permits). Any-Com can be used to mitigate the high cost of solving multi-robot problems by dividing effort among all robots the solution will benefit. This is useful when complete algorithms are desirable. Previous algorithms make assumptions about communication that are often invalid in the real world. Any-Com enables collaborative problem solving as communication permits, with graceful performance declines otherwise. This paper provides a “recipe” for Any-Com algorithms and shows results from a multi-robot path-planning and a multi-robot task allocation problem that exemplify the approach.