Towards Optimal and Expressive Kernelization for d-Hitting Set

d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example, fault diagnosis, automatic program verification, and the noise-minimizing assignment of frequencies to radio transmitters. We show a linear-time algorithm that transforms an instance of d-Hitting Set into an equivalent instance comprising at most O(k^d) hyperedges and vertices. In terms of parameterized complexity, this is a problem kernel. Our kernelization algorithm is based on speeding up the well-known approach of finding and shrinking sunflowers in hypergraphs, which yields problem kernels with structural properties that we condense into the concept of expressive kernelization. We conduct experiments to show that our kernelization algorithm can kernelize instances with more than 10^7 hyperedges in less than five minutes. Finally, we show that the number of vertices in the problem kernel can be further reduced to O(k^{d-1}) with additional O(k^{1.5 d}) processing time by nontrivially combining the sunflower technique with d-Hitting Set problem kernels due to Abu-Khzam and Moser.Comment: This version gives corrected experimental results, adds additional figures, and more formally defines "expressive kernelization

ClustalXeed: a GUI-based grid computation version for high performance and terabyte size multiple sequence alignment

Abstract Background There is an increasing demand to assemble and align large-scale biological sequence data sets. The commonly used multiple sequence alignment programs are still limited in their ability to handle very large amounts of sequences because the system lacks a scalable high-performance computing (HPC) environment with a greatly extended data storage capacity. Results We designed ClustalXeed, a software system for multiple sequence alignment with incremental improvements over previous versions of the ClustalX and ClustalW-MPI software. The primary advantage of ClustalXeed over other multiple sequence alignment software is its ability to align a large family of protein or nucleic acid sequences. To solve the conventional memory-dependency problem, ClustalXeed uses both physical random access memory (RAM) and a distributed file-allocation system for distance matrix construction and pair-align computation. The computation efficiency of disk-storage system was markedly improved by implementing an efficient load-balancing algorithm, called "idle node-seeking task algorithm" (INSTA). The new editing option and the graphical user interface (GUI) provide ready access to a parallel-computing environment for users who seek fast and easy alignment of large DNA and protein sequence sets. Conclusions ClustalXeed can now compute a large volume of biological sequence data sets, which were not tractable in any other parallel or single MSA program. The main developments include: 1) the ability to tackle larger sequence alignment problems than possible with previous systems through markedly improved storage-handling capabilities. 2) Implementing an efficient task load-balancing algorithm, INSTA, which improves overall processing times for multiple sequence alignment with input sequences of non-uniform length. 3) Support for both single PC and distributed cluster systems.</p

Fine-Grained Secure Computation

This paper initiates a study of Fine Grained Secure Computation: i.e. the construction of secure computation primitives against moderately complex adversaries. We present definitions and constructions for compact Fully Homomorphic Encryption and Verifiable Computation secure against (non-uniform) $\mathsf{NC}^1$ adversaries. Our results do not require the existence of one-way functions and hold under a widely believed separation assumption, namely $\mathsf{NC}^1 \subsetneq \oplus \mathsf{L} / \mathsf{poly}$. We also present two application scenarios for our model: (i)hardware chips that prove their own correctness, and (ii) protocols against rational adversaries potentially relevant to the Verifier\u27s Dilemma in smart-contracts transactions such as Ethereum

Partial Sums on the Ultra-Wide Word RAM

We consider the classic partial sums problem on the ultra-wide word RAM model of computation. This model extends the classic $w$-bit word RAM model with special ultrawords of length $w^2$ bits that support standard arithmetic and boolean operation and scattered memory access operations that can access $w$ (non-contiguous) locations in memory. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a new in-place data structure for the partial sum problem that only stores a constant number of ultraword in addition to the input and supports operations in doubly logarithmic time. This matches the best known time bounds for the problem (among polynomial space data structures) while improving the space from superlinear to a constant number of ultrawords. Our results are based on a simple and elegant in-place word RAM data structure, known as the Fenwick tree. Our main technical contribution is a new efficient parallel ultra-wide word RAM implementation of the Fenwick tree, which is likely of independent interest.Comment: Extended abstract appeared at TAMC 202