SAT Modulo Monotonic Theories

We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories arise from many common problems, e.g., graph properties such as reachability, shortest paths, connected components, minimum spanning tree, and max-flow/min-cut, and then demonstrate our framework by building SMT solvers for each of these theories. We apply these solvers to procedural content generation problems, demonstrating major speed-ups over state-of-the-art approaches based on SAT or Answer Set Programming, and easily solving several instances that were previously impractical to solve

Compressing DNA sequence databases with coil

Background: Publicly available DNA sequence databases such as GenBank are large, and are growing at an exponential rate. The sheer volume of data being dealt with presents serious storage and data communications problems. Currently, sequence data is usually kept in large "flat files," which are then compressed using standard Lempel-Ziv (gzip) compression – an approach which rarely achieves good compression ratios. While much research has been done on compressing individual DNA sequences, surprisingly little has focused on the compression of entire databases of such sequences. In this study we introduce the sequence database compression software coil. Results: We have designed and implemented a portable software package, coil, for compressing and decompressing DNA sequence databases based on the idea of edit-tree coding. coil is geared towards achieving high compression ratios at the expense of execution time and memory usage during compression – the compression time represents a "one-off investment" whose cost is quickly amortised if the resulting compressed file is transmitted many times. Decompression requires little memory and is extremely fast. We demonstrate a 5% improvement in compression ratio over state-of-the-art general-purpose compression tools for a large GenBank database file containing Expressed Sequence Tag (EST) data. Finally, coil can efficiently encode incremental additions to a sequence database. Conclusion: coil presents a compelling alternative to conventional compression of flat files for the storage and distribution of DNA sequence databases having a narrow distribution of sequence lengths, such as EST data. Increasing compression levels for databases having a wide distribution of sequence lengths is a direction for future work

Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Time

We give a nearly linear time randomized approximation scheme for the Held-Karp bound [Held and Karp, 1970] for metric TSP. Formally, given an undirected edge-weighted graph $G$ on $m$ edges and $\epsilon > 0$, the algorithm outputs in $O(m \log^4n /\epsilon^2)$ time, with high probability, a $(1+\epsilon)$-approximation to the Held-Karp bound on the metric TSP instance induced by the shortest path metric on $G$. The algorithm can also be used to output a corresponding solution to the Subtour Elimination LP. We substantially improve upon the $O(m^2 \log^2(m)/\epsilon^2)$ running time achieved previously by Garg and Khandekar. The LP solution can be used to obtain a fast randomized $\big(\frac{3}{2} + \epsilon\big)$-approximation for metric TSP which improves upon the running time of previous implementations of Christofides' algorithm