ACR Y HAD LTSS FROM ACR X. SYS ERROR. UNAUTH CLB THROUGH OCCUPIED ALT.

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ACR X WAS WBOUND AT FL350 5 S OF MY SOUTHERN AIRSPACE BOUNDARY. A LIMITED DATA BLOCK WAS ON MY RADAR DISPLAY. THE CTLR WORKING ACR X JUST HANDED 4 ACFT OFF TO ME THAT WERE PROCEEDING N AND NEBOUND OUT OF HIS SECTOR INTO MINE. HE VERBALLY GAVE ME CTL OF THESE ACFT. ACR Y WAS ONE OF THESE ACFT AT FL330 REQUESTING FL370 TO GET ABOVE WX THAT WAS IN THE VICINITY OF PKE. I ISSUED THE CLB; CONFLICT ALERT WENT OFF SO I TURNED ACR Y DUE N; THE OTHER CTLR TURNED ACR X S. PROBLEMS. MISCOM; APPARENTLY WHAT THE OTHER CTLR SAID TO ME AND WHAT I HEARD (WHEN CTL OF THE ACFT WAS GIVEN) WERE 2 DIFFERENT THINGS. THE OTHER CTLR GOT BUSY ON THE W SIDE OF HIS SECTOR WITH THE ACFT I WAS WORKING ON THE E SIDE OF THE SECTOR. I DIDN'T EXPECT ANOTHER ACFT TO BE GOING WBOUND (ACR X) WHEN I HAD CTL TO CLB ACFT. I DIDN'T SEE THE LIMITED DATA BLOCK FOR ACR X SO I WAS TOTALLY SURPRISED WHEN CONFLICT ALERT WENT OFF. 2 MORE SETS OF EYES WOULD HAVE SPOTTED THE POTENTIAL CONFLICT MUCH EARLIER. IN MY OPINION THIS ERROR WOULD NOT HAVE HAPPENED HAD THESE 2 SECTORS HAD D CTLRS. WE WERE BOTH 1 HOLING OUR SECTORS DUE TO SHORT STAFFING. I FEEL THAT IF A SECTOR IS OPEN IT SHOULD ALWAYS BE FULLY STAFFED. IT LOOKS TO ME LIKE THE FAA IS SACRIFICING SAFETY FOR STAFFING. THE CHIEF MADE IT CLR THAT WE CANNOT FULLY STAFF OPEN SECTORS DUE TO LIMITED PERSONNEL. HE ALSO PUT THE RESPONSIBILITY ON TO THE CTLR FOR LACK OF STAFFING BY TELLING ME THAT WHEN I'M 1 HOLING A SECTOR AND NEED HELP I SHOULD YELL FOR IT.