Toshimitsu Masuzawa

Bounding the Impact of Unbounded Attacks in Stabilization

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permit to cope with arbitrary malicious behaviors. Combining these two properties proved difficult: it is impossible to contain the spatial impact of Byzantine nodes in a self-stabilizing context for global tasks such as tree orientation and tree construction. We present and illustrate a new concept of Byzantine containment in stabilization. Our property, called Strong Stabilization enables to contain the impact of Byzantine nodes if they actually perform too many Byzantine actions. We derive impossibility results for strong stabilization and present strongly stabilizing protocols for tree orientation and tree construction that are optimal with respect to the number of Byzantine nodes that can be tolerated in a self-stabilizing context.

A self-stabilizing minimal dominating set algorithm with safe convergence

A self-stabilizing distributed system is a fault-tolerant distributed system that tolerates any kind and any finite number of transient faults, such as message loss and memory corruption. In this paper, we formulate a concept of safe convergence in the framework of self-stabilization. An ordinary self-stabilizing algorithm has no safety guarantee while it is in converging from any initial configuration. The safe convergence property guarantees that a system quickly converges to a safe configuration, and then, it gracefully moves to an optimal configuration without breaking safety. Then, we propose a minimal independent dominating set algorithm with safe convergence property. Especially, the proposed algorithm computes the lexicographically first minimal independent dominating set according to the process identifier as a priority. The priority scheme can be arbitrarily changed such as stability, battery power and/or computation power of node

A self-stabilizing link-coloring protocol resilient to byzantine faults in tree networks

Self-stabilizing protocols can tolerate any type and any number of transient faults. But self-stabilizing protocols have no guarantee of their behavior against permanent faults. Thus, investigation concerning self-stabilizing protocols resilient to permanent faults is important. This paper proposes a self-stabilizing link-coloring protocol resilient to (permanent) Byzantine faults in tree networks. The protocol assumes the central daemon, and uses Δ+1 colors where Δ is the maximum degree in the network. This protocol guarantees that, for any nonfaulty process v, if the distance from v to any Byzantine ancestor of v is greater than two, v reaches its desired states within three rounds and never changes its states after that. Thus, it achieves fault containment with radius of two. Moreover, we prove that the containment radius becomes Ω(log n) when we use only Δ colors, and prove that the containment radius becomes Ω(n) under the distributed daemon. These lower bound results prove necessity of Δ+1 colors and the central daemon to achieve fault containment with a constant radius.

Design for strong testability of RTL data paths to provide complete fault efficiency

In this paper, we propose a DFT method for RTL data paths to achieve 100% fault efficiency. The DFT method is based on hierarchical test and usage of a combinational ATPG tool. The DFT method requires lower hardware overhead and shorter test generation time than the full scan method, and also improves test application time drastically compared with the full scan method.

Fast and compact self stabilizing verification, computation, and fault detection of an MST

This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of algorithms. In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes it for improving the memory size complexity, while obtaining time efficiency too. As a result, we show that optimizing the memory size carries at most a small cost in terms of time, in the context of Minimum Spanning Tree (MST). That is, we present algorithms that are both time and space efficient for constructing an MST, for verifying it, and for detecting the location of the faults. This involves several steps that may be considered contributions in themselves. First, we generalize the notion of local proofs, trading off the locality (or, really, the time complexity) for memory efficiency. This adds a dimension to the study of distributed local proofs, that has been gaining attention recently. Second, as opposed to previous studies that presented only the labels verification part of a proof labeling schemes, we present here also a space and time efficient distributed self stabilizing marker algorithm to generates those labels. This presents proof labeling schemes as an algorithmic tool. Finally, we show how to enhance a known transformer that makes input/output algorithms self stabilizing. It now takes as input an efficient construction algorithm and an efficient self stabilizing proof labeling scheme, and produces an efficient self stabilizing algorithm. When used for MST, the transformer produces a memory optimal (i.e., O(log n) bits per node) self stabilizing algorithm, whose time complexity, namely, O(n), is significantly better even than that of previous algorithms that where not space optimal. (The time complexity of previous MST algorithms that used ©(log2 n) memory bits per node was O(n2), and the time for optimal space algorithms was O(n|E|).) Our MST algorithm also has the important property that, if faults occur after the construction ended, then they are detected by some nodes within O(log2 n) time in synchronous networks, or within O(? log2 n) time in asynchronous ones. This property is inherited from the specific proof labeling scheme we construct. It answers an open problem posed by Awerbuch and Varghese (FOCS 1991). We also show that ©(log n) time is necessary if the memory size is restricted to O(log n) bits, even in synchronous networks. Another property is that if f faults occurred, then, within the required detection time above, they are detected by some node in the O(f log n) locality of each of the faults. We also show how to improve the above detection time and locality, at the expense of some increase in the memory.

Bounding the impact of unbounded attacks in stabilization

As a new challenge of containing the unbounded influence of Byzantine processes in self-stabilizing protocols, this paper introduces a novel concept of strong stabilization. The strong stabilization relaxes the requirement of strict stabilization so that processes beyond the containment radius are allowed to be disturbed by Byzantine processes, but only a limited number of times. A self-stabilizing protocol is (t, c, f)-strongly stabilizing if any process more than c hops away from any Byzantine process is disturbed at most t times in a distributed system with at most f Byzantine processes. Here c denotes the containment radius and t denotes the containment times. The possibility and the effectiveness of the strong stabilization is demonstrated using tree orientation. It is known that the tree orientation has no strictly stabilizing protocol with a constant containment radius. This paper first shows that the problem has no constant bound of the containment radius in a tree with two Byzantine processes even when we allow processes beyond the containment radius to be disturbed any finite number of times. Then we consider the case of a single Byzantine process and present a (1, 0, 1)-strongly stabilizing protocol, which achieves optimality in both containment radius and times.

An optimal parallel algorithm for the Euclidean distance maps of 2-D binary images

Abstract This paper presents a PRAM algorithm for computing the n × n Euclidean distance map. This algorithm can be performed in O(log n) time using n 2 log n processors on the EREW PRAM and in O ( log n log log n ) time using n 2 log log n log n processors on the common CRCW PRAM, respectively. This algorithm is also applicable to many distance maps, for example, cityblock, chessboard, octagonal and chamfer distance maps.

A non-scan DFT method at register-transfer level to achieve complete fault efficiency

This paper presents a non-scan design-for-testability (DFT) method for VLSIs designed at register transfer level (RTL) to achieve complete fault efficiency. In RTL design, a VLSI generally consists of a controller and a data path. The controller and the data path are connected with internal signals: control signals and status signals. The proposed method consists of the following two steps. First, we apply our DFT methods to the controller and the data path, respectively. Then, to support at-speed testing, we append a test plan generator which generates a sequence of test control vectors for the modified data path. Our experimental results show that the proposed method can reduce significantly both of test generation time and test application time compared with the full-scan design, though the hardware overhead of our method is slightly larger than that of the full-scan design.

On byzantine containment properties of the min + 1 protocol

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a breadth-first spanning tree in this context. Combining these two properties prove difficult: we demonstrate that it is impossible to contain the impact of Byzantine processes in a strictly or strongly stabilizing manner. We then adopt the weaker scheme of topology-aware strict stabilization and we present a similar weakening of strong stabilization. We prove that the classical min+1 protocol has optimal Byzantine containment properties with respect to these criteria.

A Layout Adjustment Problem for Disjoint Rectangles Preserving Orthogonal Order

For a given set of n rectangles place on a plane, we consider a problem of finding the minimum area layout of the rectangles that avoids intersections of the rectangles and preserves the orthogonal order. Misue et al. proposed an O(n2)-time heuristic algorithm for the problem. We first show that the corresponding decision problem for this problem is NP-complete. We also present an O(n2)-time heuristic algorithm for the problem that finds a layout with smaller area than Misues.