Distributed asynchronous search with private constraints (extended abstract)

Many problem-solving tasks can be formalized as constraint saris/action problems (CSP). In a multi-agent setting, information about constraints and variables may be distributed among different agents and kept confidential. Existing algorithms for distributed constraint satisfaction consider mainly the case where access to variables is restricted to certain agents, but information about constraints can be exchanged among them. In this paper, we propose methods where constraints are private but variables can be manipulated by any agent. We describe a new algorithm for distributed CSPs, called asynchronous aggregation search (AAS). It differs from existing methods in that it treats simultaneously sets of partial solutions and it exchanges information about aggregated valuations for combinations of variables. While the approach we propose provides a more general framework for dealing with privacy requirements, its overall performance is comparable or better than that of existing methods, as shown by the experiments. 1. I N T R O D U C T I O N A distributed CSP (DCSP) arises when information is distr ibuted among several agents. In the common definition of DCSP [3], variables are distributed among agents so that each variable can only be assigned values by a single agent. Several Asynchronous Search (AS) algorithms have been developed that allow solving such problems by exchanging messages about variable assignments and conflicts with constraints (called nogoods) [3]. On the other hand, in the AS formulation, constraints may need to be revealed to any other agent that controls a variable in the corresponding constraint. This corresponds well to certain real-world situations, for example distributed control, but less well to negotiation where variables are public but constraints are private. In this paper, we consider the converse case where certain constraints are private, but the same variable can be set by many agents. Permission to make digital or hard copies of all or part of this work for personal or classroom use is &.,ranted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Agents 2000 Barcelona Spain Copyright ACM 2000 1-58113-230-1/00/6...$5.00 3•X3 Xl>X2"2 X l ~ X ,,,,1: Xl=tO_S}lO:O I ~: Xl={O..S}lO:OlX x'Z={o)lo~[ o: x3=(0,1}12:01 ,,. L • • 3: x3={o}lo:o I = 4:x2={0.1}[I:01 z.