Competitive Algorithms for Layered Graph Traversal

A layered graph is a connected graph whose vertices are partitioned into sets L0=s, L1, L2,..., and whose edges, which have nonnegative integral weights, run between consecutive layers. Its width is {|Li|}. In the on-line layered graph traversal problem, a searcher starts at s in a layered graph of unknown width and tries to reach a target vertex t; however, the vertices in layer i and the edges between layers i-1 and i are only revealed when the searcher reaches layer i-1. We give upper and lower bounds on the competitive ratio of layered graph traversal algorithms. We give a deterministic on-line algorithm which is O(9w)-competitive on width-w graphs and prove that for no w can a deterministic on-line algorithm have a competitive ratio better than 2w-2 on width-w graphs. We prove that for all w, w/2 is a lower bound on the competitive ratio of any randomized on-line layered graph traversal algorithm. For traversing layered graphs consisting of w disjoint paths tied together at a common source, we give a randomized on-line algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor

Competitive k-Server Algorithms

In this paper we give deterministic competitive k-server algorithms for all k and all metric spaces. This settles the k-server conjecture [MMS] up to the competitive ratio. The best previous result for general metric spaces was a 3-server randomized competitive algorithm [BKT] and a non-constructive proof that a deterministic 3-server competitive algorithm exists [BBKTW]. The competitive ratio we can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open.

Access Control Meets Public Key Infrastructure, Or: Assigning Roles to Strangers

The Internet enables connectivity between many strangers- entities that don't know each other. We present the Trust Policy Language (TPL), used to define the mapping of strangers to predefined business roles, based on certificates issued by third parties. TPL is expressive enough to allow complex policies, e.g. nonmonotone (negative) certificates, while being simple enough to allow automated policy checking and processing. Issuers of certificates are either known in advance, or provide sufficient certificates to be considered a trusted authority according to the policy. This allows bottom-up, ‘grass roots ’ buildup of trust, as in the real world. We extend, rather than replace, existing role-based access control mechanisms. This provides a simple, modular architecture and easy migration from existing systems. Our system automatically collects missing certificates from peer servers. In particular this allows use of standard browsers, which pass only one certificate to the server. We describe our implementation, which can be used as an extension of a web server or as a separate server with interface to applications