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The activist investor has taken a 1.7 percent stake worth about $370 million in the retailer.
Starboard is seeking majority control of the board and is also pushing for Dollar Tree to tweak its pricing model, according to the Wall Street Journal.
The hedge fund reportedly nominated seven directors to Dollar Tree's 12-member board, ahead of the nomination deadline last week.
At the center of the criticism has been Dollar Tree’s slow progress integrating and turning around Family Dollar, which it bought for $9 billion in 2015.
Starboard wants Dollar Tree to explore a sale of the struggling chain, even if it means selling it for significantly less than it paid for it, the people said.
Starboard and Dollar Tree did not immediately respond to Reuters' request for comment outside regular business hours.