Task swapping networks in distributed systems

In this paper we propose task swapping networks for task reassignments by using task swappings in distributed systems. Some classes of task reassignments are achieved by using iterative local task swappings between software agents in distributed systems. We use group-theoretic methods to find a minimum-length sequence of adjacent task swappings needed from a source task assignment to a target task assignment in a task swapping network of several well-known topologies.Comment: This is a preprint of a paper whose final and definite form is published in: Int. J. Comput. Math. 90 (2013), 2221-2243 (DOI: 10.1080/00207160.2013.772985

Symmetry and Satisfiability: An Update

Abstract. The past few years have seen significant progress in algorithms and heuristics for both SAT and symmetry detection. Additionally, the thesis that some of SAT’s intractability can be explained by the presence of symmetry, and that it can be addressed by the introduction of symmetry-breaking constraints, was tested, albeit only to a rather limited extent. In this paper we explore further connections between symmetry and satisfiability and demonstrate the existence of intractable SAT instances that exhibit few or no symmetries. Specifically, we describe a highly scalable symmetry detection algorithm based on a decision tree that combines elements of group-theoretic computation and SAT-inspired backtracking search, and provide results of its application on the SAT 2009 competition benchmarks. For SAT instances with significant symmetry we also compare SAT runtimes with and without the addition of symmetry-breaking constraints.

Smooth Projective Hashing and Two-Message Oblivious Transfer

Abstract. We present a general framework for constructing two-message oblivious transfer protocols using a modification of Cramer and Shoup’s notion of smooth projective hashing (2002). Our framework is actually an abstraction of the two-message oblivious transfer protocols of Naor and Pinkas (2001) and Aiello et. al. (2001), whose security is based on the Decisional Diffie Hellman Assumption. In particular, this framework gives rise to two new oblivious transfer protocols. The security of one is based on the N’th-Residuosity Assumption, and the security of the other is based on both the Quadratic Residuosity Assumption and the Extended Riemann Hypothesis. When using smooth projective hashing in this context, we must deal with maliciously chosen smooth projective hash families. This raises new technical difficulties that did not arise in previous applications, and in particular it is here that the Extended Riemann Hypothesis comes into play. Similar to the previous two-message protocols for oblivious transfer, our constructions give a security guarantee which is weaker than the traditional, simulation based, definition of security. Nevertheless, the security notion that we consider is nontrivial and seems to be meaningful for some applications in which oblivious transfer is used in the presence of malicious adversaries.