Synthesis of parallel adders from if-decision diagrams

Addition is one of the timing critical operations in most of modern processing units. For decades, extensive research has been done devoted to designing higher speed and less complex adder architectures, and to developing advanced adder implementation technologies. Decision diagrams are a promising approach to the efficient many-bit adder design. Since traditional binary decision diagrams does not match perfectly with the task of modelling adder architectures, other types of diagram were proposed. If-decision diagrams provide a parallel many-bit adder model with the time complexity of Ο(log2n) and area complexity of Ο(n×log2n). The paper propose a technique, which produces adder diagrams with such properties by systematically cutting the diagram’s longest paths. The if-diagram based adders are competitive to the known efficient Brent-Kung adder and its numerous modifications. We propose a blocked structure of the parallel if-diagram-based adders, and introduce an adder table representation, which is capable of systematic producing if-diagram of any bit-width. The representation supports an efficient mapping of the adder diagrams to VHDL-modules at structural and dataflow levels. The paper also shows how to perform the adder space exploration depending on the circuit fan-out. FPGA-based synthesis results and case-study comparisons of the if-diagram-based adders to the Brent-Kung and majority-invertor gate adders show that the new adder architecture leads to faster and smaller digital circuits.

A path recorder algorithm for Multiple Longest Common Subsequences (MLCS) problems

Motivation Searching the Longest Common Subsequences of many sequences is called a Multiple Longest Common Subsequence (MLCS) problem which is a very fundamental and challenging problem in many fields of data mining. The existing algorithms cannot be applicable to problems with long and large-scale sequences due to their huge time and space consumption. To efficiently handle large-scale MLCS problems, a Path Recorder Directed Acyclic Graph (PRDAG) model and a novel Path Recorder Algorithm (PRA) are proposed. Results In PRDAG, we transform the MLCS problem into searching the longest path from the Directed Acyclic Graph (DAG), where each longest path in DAG corresponds to an MLCS. To tackle the problem efficiently, we eliminate all redundant and repeated nodes during the construction of DAG, and for each node, we only maintain the longest paths from the source node to it but ignore all non-longest paths. As a result, the size of the DAG becomes very small, and the memory space and search time will be greatly saved. Empirical experiments have been performed on a standard benchmark set of both DNA sequences and protein sequences. The experimental results demonstrate that our model and algorithm outperform the related leading algorithms, especially for large-scale MLCS problems. Availability and implementation This program code is written by the first author and can be available at https://www.ncbi.nlm.nih.gov/nuccore and https://blog.csdn.net/wswguilin. Supplementary information Supplementary data are available at Bioinformatics online.

Minimum Detour Index of Tricyclic Graphs

The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. The detour index is used in various quantitative structure-property relationship and quantitative structure-activity relationship studies. In this paper, we characterize the minimum detour index among all tricyclic graphs, which attain the bounds.

Nonempty Intersection of Longest Paths in $2K_2$-Free Graphs

In 1966, Gallai asked whether all longest paths in a connected graph share a common vertex. Counterexamples indicate that this is not true in general. However, Gallai's question is positive for certain well-known classes of connected graphs, such as split graphs, interval graphs, circular arc graphs, outerplanar graphs, and series-parallel graphs. A graph is $2K_2$-free if it does not contain two independent edges as an induced subgraph. In this short note, we show that, in nonempty $2K_2$-free graphs, every vertex of maximum degree is common to all longest paths. Our result implies that all longest paths in a nonempty $2K_2$-free graph have a nonempty intersection. In particular, it strengthens the result on split graphs, as split graphs are $2K_2$-free.