Answer: There are a number of plants that might do well in moist soil, as long as it is not actually flooded with standing water. Among perennials you might try Japanese iris, Siberian iris, Monarda, Eupatorium, Filipendula, Lobelia cardinalis, Viola cucullata (can spread aggressively) as well as Chelone. There are also numerous ornamental shrubs you could use. You might consider discussing fine tuning the sprinkler system with your neighbor as it is wasting water unnecessarily and at their expense.
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