ABSTRACT: In this paper we focus on estimating the amount of information that can be embedded in the sequencing of packets in ordered
channels. Ordered channels, e.g. TCP, rely on sequence numbers to recover from packet loss and packet reordering. We propose
a formal model for transmitting information by packet-reordering. We present natural and well-motivated channel models and
jamming models including the k-distance permuter, the k-buffer permuter and the k-stack permuter. We define the natural information-theoretic (continuous) game between the channel processes (max-min) and
the jamming process (min-max) and prove the existence of a Nash equilibrium for the mutual information rate. We study the
zero-error (discrete) equivalent and provide error-correcting codes with optimal performance for the distance-bounded model,
along with efficient encoding and decoding algorithms. One outcome of our work is that we extend and complete D. H. Lehmer’s
attempt to characterize the number of distance bounded permutations by providing the asymptotically optimal bound - this also
tightly bounds the first eigen-value of a related state transition matrix.
09/2007: pages 42-57;
SPAA 2006: Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures, Cambridge, Massachusetts, USA, July 30 - August 2, 2006; 01/2006
Information Hiding, 8th International Workshop, IH 2006, Alexandria, VA, USA, July 10-12, 2006. Revised Selcted Papers; 01/2006
ABSTRACT: Consider a network in which a collection of source nodes maintain and periodically update data objects for a collec-tion of sink nodes, each of which periodically accesses the data originating from some specified subset of the source nodes. We consider the task of efficiently relaying the dy-namically changing data objects to the sinks from their sources of interest. Our focus is on the following "push-pull" approach for this data dissemination problem. Whenever a data object is updated, its source relays the update to a designated subset of nodes, its push set; similarly, whenever a sink requires an update, it propagates its query to a des-ignated subset of nodes, its pull set. The push and pull sets need to be chosen such that every pull set of a sink inter-sects the push sets of all its sources of interest. We study the problem of choosing push sets and pull sets to minimize total global communication while satisfying all communica-tion requirements. We formulate and study several variants of the above data dissemination problem, that take into account differ-ent paradigms for routing between sources (resp., sinks) and their push sets (resp., pull sets) – multicast, unicast, and controlled broadcast – as well as the aggregability of the data objects. Under the multicast model, we present an op-timal polynomial time algorithm for tree networks, which yields a randomized O(log n)-approximation algorithm for n-node general networks, for which the problem is hard to approximate within a constant factor. Under the unicast * Chakinala, Kumarasubramanian,-59593-452-9/06/0007 . model, we present a randomized O(log n)-approximation al-gorithm for non-metric costs and a matching hardness re-sult. For metric costs, we present an O(1)-approximation and matching hardness result for the case where the inter-ests of any two sinks are either disjoint or identical. Finally, under the controlled broadcast model, we present optimal polynomial-time algorithms. While our optimization problems have been formulated in the context of data communication in networks, our prob-lems also have applications to network design and multicom-modity facility location and are of independent interest.