Stand up Indulgent Gathering

Stand up indulgent gathering

“…In the continuous setting, the possibility of a robot failure was previously considered. As previously stated, the weak-gathering problem in SSYNC [1,3,6,10], and the SUIR and SUIG problems in FSYNC [4,5] were previously considered. In particular, solutions to SUIR and SUIG [4,5] make use of a level-slicing technique, that mandates them to move by a fraction of the distance to another robot.…”

“…As previously stated, the weak-gathering problem in SSYNC [1,3,6,10], and the SUIR and SUIG problems in FSYNC [4,5] were previously considered. In particular, solutions to SUIR and SUIG [4,5] make use of a level-slicing technique, that mandates them to move by a fraction of the distance to another robot. Obviously, such a technique cannot be translated to the discrete model, where robots always move by exactly one edge.…”

“…We consider the Stand Up Indulgent Gathering (SUIG) problem defined in [5]. An algorithm solves the SUIG problem if, for any initial configuration C 0 (that may contain multiplicities), and for any execution E = (C 0 , C 1 , .…”

“…Our positive results are constructive, as we provide an algorithm for each case and prove it correct. As expected, the key enabling algorithmic constructions we use for our protocols are fundamentally different from those used in continuous spaces [4,5], as robots can no longer use fractional moves to solve the problem, and can be of independent interest to build further solutions in other topologies.…”

“…Two variants have been studied: weak gathering expects all correct (non-crashed) robots to gather regardless of crashed robot positions, while strong gathering (also known as stand-up indulgent gathering -SUIG) expects correct robots to gather at the unique crash location. In continuous Euclidean space, weak gathering is solvable in the SSYNC model [1,3,8,9], while SUIG (and its two-robot variant, stand-up indulgent rendezvous -SUIR) is only solvable in the FSYNC model [5,6,7].…”