Lesley R. Matheson

Resistance of digital watermarks to collusive attacks

In digital watermarking (also called digital fingerprinting), extra information is embedded imperceptibly into digital content (such as an audio track, a still image, or a movie). This extra information can be read by authorized parties, and other users attempting to remove the watermark cannot do so without destroying the value of the content by making perceptible changes to the content. This provides a disincentive to copying by allowing copies to be traced to their original owner. Unlike cryptography, digital watermarking provides protection to content that is in the clear. It is not easy to design watermarks that are hard to erase, especially if an attacker has access to several differently marked copies of the same base content. Cox et al. (see IEEE Trans. on Image Processing, vol.6, no.12, p.1673-87, 1997) have proposed the use of additive normally distributed values as watermarks, and have sketched an argument showing that, in a certain theoretical model, such watermarks are resistant to collusive attacks. Here, we fill in the mathematical justification for this claim.

Models of parallel computation: a survey and synthesis

In the realm of sequential computing, the random access machine has successfully provided an underlying model of computation that has promoted consistency and coordination among algorithm developers, computer architects and language experts. In the realm of parallel computing, however, there has been no similar success. The need for such a unifying parallel model or set of models is heightened by the greater demand for performance and the greater diversity among machines. Yet the modeling of parallel computing still seems to be mired in controversy and chaos. This paper presents a broad range of models of parallel computation and the different roles they serve in algorithm, language and machine design. The objective is to better understand which model characteristics are important to each design community, in order to elucidate the requirements of a unifying paradigm. As an impetus for discussion, we conclude by suggesting a model of parallel computation which is consistent with a model design philosophy that balances simplicity and descriptivity with prescriptivity. We present only the survey of abstract computational models. This introduction should provide insights into the rich array of relevant issues in other disciplines.<<ETX>>

Dominating sets in planar graphs

Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Specifically, we wish to find the smallestesuch that, fornsufficiently large, everyn-vertex planar graph contains a dominating set of size at mosten.We prove that 1/4<e<1/3, and we conjecture thate=1/4.For triangulated discs we obtain a tight bound ofe=1/3.The upper bound proof yields a linear-time algorithm for finding an(n/3)-size dominating set.

Dynamic Self-Checking Techniques for Improved Tamper Resistance

We describe a software self-checking mechanism designed to improve the tamper resistance of large programs. The mechanism consists of a number of testers that redundantly test for changes in the executable code as it is running and report modifications. The mechanism is built to be compatible with copy-specific static watermarking and other tamper-resistance techniques. The mechanism includes several innovations to make it stealthy and more robust.

Robustness and Security of Digital Watermarks

Digital watermarking is a nascent but promising technology that offers protection of unencrypted digital content. This paper is a brief technical survey of the multimedia watermarking landscape. The three main technical challenges faced by watermarking algorithms are fidelity, robustness and security. Current watermarking methods offer possibly acceptable fidelity and robustness against certain types of processing, such as data compression and noise addition, but are not sufficiently robust against geometric transforms such as scaling and cropping of images. Theoretical approaches have been developed that could lead to secure watermarking methods, but substantial gaps remain between theory and practice.

Culturally induced information impactedness: a prescription for failure in software ventures

The impact of effective information flow in software ventures is analyzed through a recent case in which a hot, lucrative technology was lost on its way to the marketplace. The failure occurred despite the fact that the venture had many components crucial to success, including a proprietary intellectual property position, enormous market demand, a well-qualified, committed team, and sufficient funding. One reason for this failure is the lack of information flows among several parties critical to the success of the venture. This case suggests that in software markets that operate at breakneck pace and have short development cycles, effective information flow is a first-order priority. These blockages in information flows can stem from the nature of the cultures that are created to produce software ideas, especially proprietary technologies. The case also suggests that information can be affected by the clash between U.S. software market characteristics and Japanese business culture. Fortunately, there are inexpensive solutions that can substantially improve the return on investment, especially foreign investment, in new software technologies.

Parallelism in multigrid methods: how much is too much?

Multigrid methods are powerful techniques to accelerate the solution of computationally-intensive problems arising in a broad range of applications. Used in conjunction with iterative processes for solving partial differential equations, multigrid methods speed up iterative methods by moving the computation from the original mesh covering the problem domain through a series of coarser meshes. But this hierarchical structure leaves domain-parallel versions of the standard multigrid algorithms with a deficiency of parallelism on coarser grids. To compensate, several parallel multigrid strategies with more parallelism, but also more work, have been designed. We examine these parallel strategies and compare them to simpler standard algorithms to try to determine which techniques are more efficient and practical. We consider three parallel multigrid strategies: (1) domain-parallel versions of the standard V-cycle and F-cycle algorithms; (2) a multiple coarse grid algorithm, proposed by Fredrickson and McBryan, which generates several coarse grids for each fine grid; and (3) two Rosendale algorithm, which allow computation on all grids simultaneously. We study an elliptic model problem on simple domains, discretized with finite difference techniques on block-structured meshes in two or three dimensions with up to 106 or 109 points, respectively. We analyze performance using three models of parallel computation: the PRAM and two bridging models. The bridging models reflect the salient characteristics of two kinds of parallel computers: SIMD fine-grain computers, which contain a large number of small (bitserial) processors, and SPMD medium-grain computers, which have a more modest number of powerful (single chip) processors. Our analysis suggests that the standard algorithms are substantially more efficient than algorithms utilizing either parallel strategy. Both parallel strategies need too much extra work to compensate for their extra parallelism. They require a highly impractical number of processors to be competitive with simpler, standard algorithms. The analysis also suggests that the F-cycle, with the appropriate optimization techniques, is more efficient than the V-cycle under a broad range of problem, implementation, and machine characteristics, despite the fact that it exhibits even less parallelism than the V-cycle.

Analysis of Multigrid Algorithms on Massively Parallel Computers

We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether currently envisioned machines will provide an efficient platform for such algorithms. These algorithms substantially improve the performance of iterative methods of solving partial differential equations. We consider the domain parallel version of the standard V-cycle multigrid algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block-structured grids of size 106and 109, respectively. We develop a set of models of parallel computation which reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, “workstation size” processors executing in a SPMD mode. The models, based on the computing characteristics of an architectural class, provide metrics which balance abstraction with machine specificity. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests that an efficient implementation for practical problem sizes requires the machine to support the efficient transmission of long messages (up to 1000 words); otherwise the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. The analysis also suggests that low diameter multistage networks provide little or no advantage over a simple single stage communications network. Finally, the analysis suggests that fine grain parallelism and low fixed communication costs may provide more efficiency than medium grain parallelism with low variable communications costs.

Toward Efficient Unstructured Multigrid Preprocessing

The multigrid method is a general and powerful means of accelerating the convergence of discrete iterative methods for solving partial differential equations (PDEs) and similar problems. The adaptation of the multigrid method to un structured meshes is important in solving problems with complex geometries. Such problems lie on the forefront of many scientific and engineering fields. Unfortunately, multi grid schemes on unstructured meshes require signifi cantly more preprocessing than on structured meshes. In fact, preprocessing can be a major part of the solution task and, for many applications, must be executed repeatedly. In addition, the large computational requirements of real istic PDEs, accurately discretized on unstructured meshes, make such computations candidates for parallel or distributed processing. This adds problem partitioning as a preprocessing task. We propose and examine experi mentally an automatic and unified strategy to perform several unstructured multigrid preprocessing tasks. Our strategy is based on dominating sets in the unstructured meshes. We also suggest several alternative related strategies. Our experiments evaluate the performance of two preprocessing tasks: coarse-mesh generation and domain partitioning. The experiments suggest that our preprocessing strategy produces high-quality meshes that give good multigrid performance. Our strategy also pro duces domain partitions that are reasonably load bal anced with relatively small edge cuts. Overall, we conclude that simple, integrated algorithmic strategies and data structures can make tedious preprocessing tasks more efficient and more automated—a necessary step toward the practical application of unstructured multigrid methods.

Toward Efficient Unstructured Multigrid Preprocessing (Extended Abstract)

The multigrid method is a general and powerful means of accelerating the convergence of discrete iterative methods for solving partial differential equations (PDEs) and similar problems. The adaptation of the multigrid method to unstructured meshes is important in the solution of problems with complex geometries. Unfortunately, multigrid schemes on unstructured meshes require significantly more preprocessing than on structured meshes. In fact, preprocessing can be a major part of the solution task, and for many applications, must be done repeatedly. In addition, the large computational requirements of realistic PDEs, accurately discretized on unstructured meshes, make such computations candidates for parallel or distributed processing, adding problem partitioning as a preprocessing task.