Abstract :
In this paper, we present an O(1) time algorithm to solve the minimum coloring problem defined on a set of intervals, which is also called the channel assignment problem. This problem has not been solved in O(1) time before, even on the idealistic CRCW PRAM model. For large-sized problems, it is desirable to have fast hardware-solutions. Our algorithm is based on the processor arrays with a reconfigurable bus system (abbreviated to PARBS) that consists of a processor array and a reconfigurable bus system. In order to solve this problem with constant time complexity, we first transform the “left-edge” channel assignment algorithm to the parenthesis-matching problem. Based on this novel scheme, we are able to explore constant-time parallel algorithms to solve the minimum coloring problem for n intervals, which is also called the channel assignment problem, on a PARBS with O(n2) processors
Keywords :
VLSI; computational complexity; graph colouring; multiprocessor interconnection networks; parallel algorithms; reconfigurable architectures; CRCW PRAM model; O(1) time algorithm; PARBS; VLSI processor array; channel assignment algorithm; channel assignment problem; constant time complexity; constant-time algorithms; constant-time parallel algorithms; fast hardware-solutions; large-sized problems; minimum coloring problem; parenthesis-matching problem; processor array; processor arrays; reconfigurable bus system; reconfigurable bus systems; Algorithm design and analysis; Automata; Computational modeling; Concurrent computing; Hardware; Helium; Parallel algorithms; Parallel processing; Phase change random access memory; Very large scale integration;
