Michael J. Nelson

Bio: Michael J. Nelson is an academic researcher from University of California, Irvine. The author has contributed to research in topics: Data structure & Degree (graph theory). The author has an hindex of 4, co-authored 5 publications receiving 192 citations. Previous affiliations of Michael J. Nelson include IBM.

Fundamental parallel algorithms for private-cache chip multiprocessors

Abstract: In this paper, we study parallel algorithms for private-cache chip multiprocessors (CMPs), focusing on methods for foundational problems that are scalable with the number of cores. By focusing on private-cache CMPs, we show that we can design efficient algorithms that need no additional assumptions about the way cores are interconnected, for we assume that all inter-processor communication occurs through the memory hierarchy. We study several fundamental problems, including prefix sums, selection, and sorting, which often form the building blocks of other parallel algorithms. Indeed, we present two sorting algorithms, a distribution sort and a mergesort. Our algorithms are asymptotically optimal in terms of parallel cache accesses and space complexity under reasonable assumptions about the relationships between the number of processors, the size of memory, and the size of cache blocks. In addition, we study sorting lower bounds in a computational model, which we call the parallel external-memory (PEM) model, that formalizes the essential properties of our algorithms for private-cache CMPs.

The rainbow skip graph: a fault-tolerant constant-degree distributed data structure

Abstract: We present a distributed data structure, which we call the rainbow skip graph. To our knowledge, this is the first peer-to-peer data structure that simultaneously achieves high fault-tolerance, constant-sized nodes, and fast update and query times for ordered data. It is a non-trivial adaptation of the SkipNet/skip-graph structures of Harvey et al. and Aspnes and Shah, so as to provide fault-tolerance as these structures do, but to do so using constant-sized nodes, as in the family tree structure of Zatloukal and Harvey. It supports successor queries on a set of n items using O(log n) messages with high probability, an improvement over the expected O(log n) messages of the family tree. Our structure achieves these results by using the following new constructs:• Rainbow connections: parallel sets of pointers between related components of nodes, so as to achieve good connectivity between "adjacent" components, using constant-sized nodes.• Hydra components: highly-connected, highly fault-tolerant components of constant-sized nodes, which will contain relatively large connected subcomponents even under the failure of a constant fraction of the nodes in the component.We further augment the hydra components in the rainbow skip graph by using erasure-resilient codes to ensure that any large subcomponent of nodes in a hydra component is sufficient to reconstruct all the data stored in that component. By carefully maintaining the size of related components and hydra components to be O(log n), we are able to achieve fast times for updates and queries in the rainbow skip graph. In addition, we show how to make the communication complexity for updates and queries be worst case, at the expense of more conceptual complexity and a slight degradation in the node congestion of the data structure.

The Rainbow Skip Graph: A Fault-Tolerant Constant-Degree P2P Relay Structure

Abstract: We present a distributed data structure, which we call the rainbow skip graph. To our knowledge, this is the first peer-to-peer data structure that simultaneously achieves high fault tolerance, constant-sized nodes, and fast update and query times for ordered data. It is a non-trivial adaptation of the SkipNet/skip-graph structures of Harvey et al. and Aspnes and Shah, so as to provide fault-tolerance as these structures do, but to do so using constant-sized nodes, as in the family tree structure of Zatloukal and Harvey. It supports successor queries on a set of n items using O(log n) messages with high probability, an improvement over the expected O(log n) messages of the family tree.

Adaptive traitor tracing for large anonymous attack

Abstract: In this paper we focus on traitor tracing technologies for the anonymous re-broadcasting attack where the attackers re-distribute the per-content encrypting key or the decrypted plain content. To defend against an anonymous attack, content is usually built with different variations. For example, content is divided into multiple segments, each segment comes with multiple variations, and each variation is differently encrypted. Each user/player can only play back one variation per segment through the content.A typical traitor tracing scheme for re-broadcasting attack involves two basic steps, assigning the key/variation to devices (the assignment step) and detecting at least one traitor in the coalition when a series of pirated key/content are recovered (the coalition detection step). The traceability of a traitor tracing scheme is defined to be the number of recovered pirate copies of the content/keys needed in order to detect traitors. In [1] we presented a traitor detection scheme that tries to detect the entire coalition all together. This significantly improved the traditional one-by-one detection approaches in the literature. However, the traceability of the traitor detection scheme has a up limit that is constrained by the number of variations q one can build into the content. We are motivated to improve the traceability on a larger collusion attack and lift the up-limit on traceability with a given q. In this paper we will show a new traitor tracing approach that will assign the variations with skewed probabilities. Our approach not only lifts the tracing up-limit but also enables the tracing agency to assign the variations so as to maximize the traceability for a given coalition size. Our traceability results show that it is possible to achieve good traceability when traitor size exceeds q, and continue doing well even after the coalition size reaches q log q.

Adaptive traitor tracing

Abstract: One embodiment of the present invention includes a method for traitor tracing that selects a probability distribution for the assignment of file-segment variations in a digital file. This probability distribution is selected to improve traceability for a particular size of a coalition of attackers. At least one symbol for each file-segment variation is then distributed based on the selected probability distribution.

Efficient and Robust Approximate Nearest Neighbor Search Using Hierarchical Navigable Small World Graphs

Abstract: We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures (typically used at the coarse search stage of the most proximity graph techniques). Hierarchical NSW incrementally builds a multi-layer structure consisting of a hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting the search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Algorithms and Data Structures for External Memory

Abstract: Data sets in large applications are often too massive to fit completely inside the computer's internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. In this manuscript, we survey the state of the art in the design and analysis of algorithms and data structures for external memory (or EM for short), where the goal is to exploit locality and parallelism in order to reduce the I/O costs. We consider a variety of EM paradigms for solving batched and online problems efficiently in external memory. For the batched problem of sorting and related problems like permuting and fast Fourier transform, the key paradigms include distribution and merging. The paradigm of disk striping offers an elegant way to use multiple disks in parallel. For sorting, however, disk striping can be nonoptimal with respect to I/O, so to gain further improvements we discuss distribution and merging techniques for using the disks independently. We also consider useful techniques for batched EM problems involving matrices, geometric data, and graphs. In the online domain, canonical EM applications include dictionary lookup and range searching. The two important classes of indexed data structures are based upon extendible hashing and B-trees. The paradigms of filtering and bootstrapping provide convenient means in online data structures to make effective use of the data accessed from disk. We also re-examine some of the above EM problems in slightly different settings, such as when the data items are moving, when the data items are variable-length such as character strings, when the data structure is compressed to save space, or when the allocated amount of internal memory can change dynamically. Programming tools and environments are available for simplifying the EM programming task. We report on some experiments in the domain of spatial databases using the TPIE system (Transparent Parallel I/O programming Environment). The newly developed EM algorithms and data structures that incorporate the paradigms we discuss are significantly faster than other methods used in practice.

Low depth cache-oblivious algorithms

Abstract: In this paper we explore a simple and general approach for developing parallel algorithms that lead to good cache complexity on parallel machines with private or shared caches. The approach is to design nested-parallel algorithms that have low depth (span, critical path length) and for which the natural sequential evaluation order has low cache complexity in the cache-oblivious model. We describe several cache-oblivious algorithms with optimal work, polylogarithmic depth, and sequential cache complexities that match the best sequential algorithms, including the first such algorithms for sorting and for sparse-matrix vector multiply on matrices with good vertex separators.Using known mappings, our results lead to low cache complexities on shared-memory multiprocessors with a single level of private caches or a single shared cache. We generalize these mappings to multi-level cache hierarchies of private or shared caches, implying that our algorithms also have low cache complexities on such hierarchies. The key factor in obtaining these low parallel cache complexities is the low depth of the algorithms we propose.

Efficient Content Authentication in Peer-to-Peer Networks

Abstract: We study a new model for data authentication over peer-to-peer (p2p) storage networks, where data items are stored, queried and authenticated in a totally decentralized fashion. The model captures the security requirements of emerging distributed computing applications. We present an efficient construction of a distributed Merkle tree(DMT), which realizes an authentication tree over a p2p network, thus extending a fundamental cryptographic technique to distributed environments. We show how our DMT can be used to design an authenticated distributed hash tablethat is secure against replay attacks and consistent with the update history. Our scheme is built on top of a broad class of existing p2p overlay networks and achieves generality by using only the basic functionality of object location. We use this scheme to design the first efficient distributed authenticated dictionary.