A Hardware Relaxation Paradigm for Solving NP-Hard Problems
نویسندگان
چکیده
Digital circuits with feedback loops can solve some instances of NP-hard problems by relaxation: the circuit will either oscillate or settle down to a stable state that represents a solution to the problem instance. This approach differs from using hardware accelerators to speed up the execution of deterministic algorithms, as it exploits stabilisation properties of circuits with feedback, and it allows a variety of hardware techniques that do not have counterparts in software. A feedback circuit that solves many instances of Boolean satisfiability problems is described, with experimental results from a preliminary simulation using a hardware accelerator.
منابع مشابه
LP Relaxations of Some NP-Hard Problems Are as Hard as Any LP
We show that solving linear programming (LP) relaxations of many classical NP-hard combinatorial optimization problems is as hard as solving the general LP problem. Precisely, the general LP can be reduced in linear time to the LP relaxation of each of these problems. This result poses a fundamental limitation for designing efficient algorithms to solve the LP relaxations, because finding such ...
متن کاملParallelizing Assignment Problem with DNA Strands
Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...
متن کاملBike sharing systems: Solving the static rebalancing problem
This paper deals with a new problem that is a generalization of the many to many pickup and delivery problem and which is motivated by operating self-service bike sharing systems. There is only one commodity, initially distributed among the vertices of a graph, and a capacitated single vehicle aims to redistribute the commodity in order to reach a target distribution. Each vertex can be visited...
متن کاملA multi-criteria vehicle routing problem with soft time windows by simulated annealing
This paper presents a multi-criteria vehicle routing problem with soft time windows (VRPSTW) to mini-mize fleet cost, routes cost, and violation of soft time windows penalty. In this case, the fleet is heterogene-ous. The VRPSTW consists of a number of constraints in which vehicles are allowed to serve customers out of the desirable time window by a penalty. It is assumed that this relaxation a...
متن کاملA reactive bone route algorithm for solving the traveling salesman problem
The traveling salesman problem (TSP) is a well-known optimization problem in graph theory, as well as in operations research that has nowadays received much attention because of its practical applications in industrial and service problems. In this problem, a salesman starts to move from an arbitrary place called depot and after visits all of the nodes, finally comes back to the depot. The obje...
متن کامل