A domain-independent heuristic function created by an abstraction is usually implemented using a Pattern Database (PDB), which is a lookup table of (abstract state, heuristic value) pairs. PDBs containing high quality heuristic values generally require substantial memory space and therefore need to be compressed. In this paper, we introduce Acyclic Random Hypergraph Compression (ARHC), a domain-independent approach to compressing PDBs using acyclic random r-partite r-uniform hypergraphs. The ARHC algorithm, which comes in Base and Extended versions, provides fast lookup and a high compression rate. ARHC-Extended achieves higher quality heuristics than ARHC-Base by decreasing the heuristic information loss at the cost of some decrease in the compression rate. ARHC shows higher performance than level-by-level Bloom filter PDB compression in all experiments conducted so far.