18896215
Hamiltonicity of regular graphs and blocks of consecutive ones in symmetric matrices
We show that the Hamiltonicity of a regular graph G can be fully characterized by the numbers of blocks of consecutive ones in the binary matrix A+I, where A is the adjacency matrix of G, I is the unit matrix, and the blocks can be either linear or circular. Concretely, a k-regular graph G with girth g(G)>=5 has a Hamiltonian circuit if and only if the matrix A+I can be permuted on rows such that each column has at most (or exactly) k-1 circular blocks of consecutive ones; and if the graph G is k-regular except for two (k-1)-degree vertices a and b, then there is a Hamiltonian path from a to b if and only if the matrix A+I can be permuted on rows to have at most (or exactly) k-1 linear blocks per column. Then we turn to the problem of determining whether a given matrix can have at most k blocks of consecutive ones per column by some row permutation. For this problem, Booth and Lueker gave a linear algorithm for k=1 [Proceedings of the Seventh Annual ACM Symposium on Theory of Computing, 1975, pp. 255-265]; Flammini et al. showed its NP-completeness for general k [Algorithmica 16 (1996) 549-568]; and Goldberg et al. proved the same for every fixed k>=2 [J. Comput. Biol. 2 (1) (1995) 139-152]. In this paper, we strengthen their result by proving that the problem remains NP-complete for every constant k>=2 even if the matrix is restricted to (1) symmetric, or (2) having at most three blocks per row.
8121247
On the hardness of minimizing space for all-shortest-path interval routing schemes
k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc; and global k-IRS allows not more than a total of k interval labels in the whole network. A fundamental problem is to characterize the networks that admit k-IRS (or global k-IRS). Many of the problems related to single-shortest-path k-IRS have already been shown to be NP-complete. For all-shortest-path k-IRS, the characterization problem remains open for k>=1. In this paper, we study the time complexity of devising minimal-space all-shortest-path k-IRSs and show that it is NP-complete to decide whether a graph admits an all-shortest-path k-IRS, for every integer k>=3, and so is that of deciding whether a graph admits an all-shortest-path k-strict IRS, for every integer k>=4. These are the first NP-completeness results for all-shortest-path k-IRS where k is a constant and the graph is unweighted. The NP-completeness holds also for the linear case. We also prove that it is NP-complete to decide whether an unweighted graph admits an all-shortest-path IRS with global compactness of at most k, which also holds for the linear and strict cases.
42750715
NP-Completeness Results for All-Shortest-Path Interval Routing
k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc. A fundamental problem is to characterize the networks that admit k-IRS. Many of the problems related to single-shortest-path k-IRS have already been shown to be NP-complete. For all-shortest-path k-IRS, the characterization problem remains open for k≥ 1. We investigate the time complexity of devising minimal-space all-shortest-path k-IRS and prove that it is NP-complete to decide whether a graph admits an all-shortest-path k-IRS, for every integer k≥ 3, as well as whether a graph admits an all-shortest-path k-strict IRS, for every integer k≥ 4. These are the first NP-completeness results for all-shortest-path k-IRS where k is a constant and the graph is unweighted. Moreover, the NP-completeness holds also for the linear case.
14833504
Optimal gossiping in square 2D meshes
Gossiping is the communication problem in which each node has a unique message to be transmitted to every other node. The nodes exchange their message by packets. A solution to the problem is judged by how many rounds of packet sending it requires. In this paper, we consider the version of the problem in which small-size packets each carrying exactly one message are used. The nodes of the target meshes are assumed to be all-port (a node's incident edges can all be active at the same time); and their edges are either half-duplex or full-duplex, which are also known as the H* model and the F* model, respectively. We study the class of 2D square meshes. Soch and Tvrdik (SIROCCO'97, pp. 253-265; Tech. rep. DC-97-04, Dept. of CS&E, Czech Technical University) have obtained optimal algorithms for the F* model (for square or nonsquare meshes). Lau and Zhang (IEEE Trans. Parallel Distribut. Syst. 13 (4) (2002) 349-358) have obtained fast algorithms for the H* model. We present optimal algorithms for both models, with the interesting property that they route their messages along the same paths and in the same order, i.e. for any edge {u,v}, the i-th message from u to v under either model is the same message.
8091014
Learning your identity and disease from research papers: information leaks in genome wide association study
Genome-wide association studies (GWAS) aim at discovering the association between genetic variations, particularly single-nucleotide polymorphism (SNP), and common diseases, which is well recognized to be one of the most important and active areas in biomedical research. Also renowned is the privacy implication of such studies, which has been brought into the limelight by the recent attack proposed by Homer et al. Homer's attack demonstrates that it is possible to identify a GWAS participant from the allele frequencies of a large number of SNPs. Such a threat, unfortunately, was found in our research to be significantly understated. In this paper, we show that individuals can actually be identified from even a relatively small set of statistics, as those routinely published in GWAS papers. We present two attacks. The first one extends Homer's attack with a much more powerful test statistic, based on the correlations among different SNPs described by coefficient of determination (r2). This attack can determine the presence of an individual from the statistics related to a couple of hundred SNPs. The second attack can lead to complete disclosure of hundreds of participants' SNPs, through analyzing the information derived from published statistics. We also found that those attacks can succeed even when the precisions of the statistics are low and part of data is missing. We evaluated our attacks on the real human genomes and concluded that such threats are completely realistic.
3390974
All-frequency interactive relighting of translucent objects with single and multiple scattering
We present a technique, based on precomputed light transport, for interactive rendering of translucent objects under all-frequency environment maps. We consider the complete BSSRDF model proposed by Jensen et al. [2001]. which includes both single and diffuse multiple scattering components. The challenge is how to efficiently precompute all-frequency light transport functions due to subsurface scattering. We apply the two-pass hierarchical technique by Jensen et al. [2002] in the space of non-linearly approximated transport vectors, which allows us to efficiently evaluate transport vectors due to diffuse multiple scattering. We then include an approximated single scattering term in the precomputation, which previous interactive systems have ignored. For an isotropic phase function, this approximation produces a diffuse transport vector per vertex, and is combined with the multiple scattering component. For a general phase function, we introduce a technique from BRDF rendering to factor the phase function using a separable decomposition to allow for view-dependent rendering. We show that our rendering results qualitatively match the appearance of translucent objects, achieving a high level of realism at interactive rates.
8634013
Fast, Sub-pixel Antialiased Shadow Maps
Solving aliasing artifacts is an essential problem in shadow mapping approaches. Many works have been proposed, however, most of them focused on removing the texel-level aliasing that results from the limited resolution of shadow maps. Little work has been done to solve the pixel-level shadow aliasing that is produced by the rasterization on the screen plane. In this paper, we propose a fast, sub-pixel antialiased shadowing algorithm to solve the pixel aliasing problem. Our work is based on the alias-free shadow maps, which is capable of computing accurate per-pixel shadow, and only incurs little cost to extend to sub-pixel accuracy. Instead of direct supersampling the screen space, we take facets to approximate pixels in shadow testing. The shadowed area of one facet is rapidly evaluated by projecting blocker geometry onto a supersampled 2D occlusion mask with bitmasks fusion. It provides a sub-pixel occlusion sampling so as to capture fine shadow details and features. Furthermore, we introduce the silhouette mask map that limits visibility evaluation to pixels only on the silhouette, which greatly reduces the computation cost. Our algorithm runs entirely on the GPU, achieving real-time performance and is an order of magnitude faster than the brute-force supersampling method to produce comparable 32× antialiased shadows.
33253402
An efficient GPU-based approach for interactive global illumination
This paper presents a GPU-based method for interactive global illumination that integrates complex effects such as multi-bounce indirect lighting, glossy reflections, caustics, and arbitrary specular paths. Our method builds upon scattered data sampling and interpolation on the GPU. We start with raytraced shading points and partition them into coherent shading clusters using adaptive seeding followed by k-means. At each cluster center we apply final gather to evaluate its incident irradiance using GPU-based photon mapping. We approximate the entire photon tree as a compact illumination cut, thus reducing the final gather cost for each ray. The sampled irradiance values are then interpolated at all shading points to produce rendering. Our method exploits the spatial coherence of illumination to reduce sampling cost. We sample sparsely and the distribution of sample points conforms with the underlying illumination changes. Therefore our method is both fast and preserves high rendering quality. Although the same property has been exploited by previous caching and adaptive sampling methods, these methods typically require sequential computation of sample points, making them ill-suited for the GPU. In contrast, we select sample points adaptively in a single pass, enabling parallel computation. As a result, our algorithm runs entirely on the GPU, achieving interactive rates for scenes with complex illumination effects.
18276513
Decentralized Fair Resource Allocation for Relay-Assisted Cognitive Cellular Downlink Systems
In this paper, we consider a relay-assisted cognitive cellular downlink system dynamically accessing a spectrum licensed to a primary network, thereby improving the efficiency of spectrum usage. A cluster-based relay-assisted architecture is proposed, where relay stations are employed for minimizing the interference to users in the primary network and achieving fairness for cell-edge users. Based on this architecture, an optimal solution is derived for jointly controlling data rate, transmission power, and subband allocation to optimize the weighted sum goodput where proportional fair scheduling (PFS) is included as a special case. As shown by simulations, the proposed solution achieves significant throughput gains and better user fairness compared with existing designs.