The Complexity of Reconfiguring Network Models

Abstract

This paper concerns some of the theoretical complexity aspects of the reconfigurable network model. The computational power of the model is investigated under several variants, depending on the type of switches (or switch operations) assumed by the network nodes. Computational power is evaluated by focusing on the set of problems computable in constant time in each variant. A hierarchy of such problem classes corresponding to different variants is shown to exist and is placed relative to traditional classes of complexity theory.

Undirected ST-connectivity in log-space

“…al. [47], and putting some very interesting problems into SL. To give just one example, the planarity of bounded-degree undirected graphs was placed in SL as a corollary (we refer again to [8] for a list of SL-complete problems).…”

Constant time dynamic programming on directed reconfigurable networks

“…These results assure that adding directed links to the linear models of reconfiguration doesn't improve their computational power. The same problem for the RN model is open and strongly related to some profound theoretical complexity issues, as shown in [2]. Indeed, a result similar to Lemma 2.1 for the DRN model would imply that LOGSPACE is equal to NLOGSPACE, thus closing one of the most known and important open questions in Complexity Theory.…”

“…7. By propagating along the subbuses, the signals iteratively perform the operation of (3) which is exactly equal to (2). Indeed, the architecture does have feedback loops which allow to mimic the iterative nature of the Bellman-Ford algorithm.…”

Fast, Efficient Mutual and Self Simulations for Shared Memory and Reconfigurable Mesh

“…Hence a bus may consist of any connected sub-graph. In [5,451 it was shown that the set of problems computable in constant time on a polynomial size Linear-RMESH is exactly the set of problems computable by a logspace Turing machine, whereas the corresponding set for the General-RMESH contains exactly all the problems that are computable by a logspace Turing machine having a symmetric logspace oracle. Thus the General-RMESH is expected to be more powerful than the Linear-RMESH.…”

“…Indeed, the model captures features of '196 Y. MATIAS AND A. SCHUSTER many commercial and experimental machines, which offer flexible communication patterns. The increasing interest in the RMESH has resulted in a rapidly expanding volume of algorithmic and theoretical results; see for example [3,4,5,401. It has been shown that the RMESH can solve some fundamental problems very fast.…”