In this paper, we study the classic and well-studied longest common subsequence (LCS) problem and a recent variant of it namely constrained LCS (CLCS) problem. In CLCS, the computed LCS must also be a supersequence of a third given string. In this paper, we first present an efficient algorithm for the traditional LCS problem that runs in O(R log log n + n) time, where R is the total number of o...

We study homomorphic hash functions into SL2(q), the 2 × 2 matrices with determinant 1 over the field with q elements. Modulo a well supported number theoretic hypothesis, which holds in particular for all concrete homomorphisms proposed thus far, we prove that a random homomorphism is at least as secure as any concrete homomorphism. For a family of homomorphisms containing several concrete pro...

A sequence of integers x, <x2 < < xk is called an ascending wave of length k if x~+~-x~<x~+~--~~+~ for all 1 < ig k-2. Let f(k) be the smallest positive integer such that any 2-coloring of { 1,2, . . . . f(k)} contains a monochromatic ascending wave of length k. Settling a problem of Brown, Erdiis, and Freedman we show that there are two positive constants c ,, c2 such that c,k3<f(k)<c2k3 for a...

We present a randomized algorithm that, on input a weakly diagonally dominant symmetric n-by-n matrix A with m non-zero entries and an n-vector b, produces an x̃ such that ‖x − x̃‖ A ≤ ǫ ‖x‖ A , where Ax = b, in expected time m log n log(1/ǫ). The algorithm applies subgraph preconditioners in a recursive fashion. These preconditioners improve upon the subgraph preconditioners first introduced by ...

the effects of irrigation methods, various levels of water and nitrogen fertilizer on quality of cotton were studied at hashemabad cotton research station of gorgan in 2008. the experiment was conducted in split-split plot design with three replications. irrigation methods of furrow and sprinkler were main plots, various levels of water of 0%, 33%, 66%, 100% and 133% were subplots plots and var...

Absrract.-Log length exerted a critical influence in stabilizing large woody debris (LWD) pieces added as an experimental stream restoration technique. Logs longer than the average bank-full channel width (5.5 m) were significantly less likely to be displaced than logs shorter than this width. The longest log in stable log groups was significantly longer than the longest log in unstable groups....

An investigation of the population parameters of Indian mackerel, Rastrelliger kanagurta (Cuvier, 1816) in the Marudu Bay, Sabah, Malaysia was carried out from January to September 2013. The relationship between total length and body weight was estimated as W=0.006TL3.215 or Log W=3.215LogTL – 2.22 (R2=0.946). Monthly length frequency data of R. kanagurta were analyzed by FiSAT software to eva...

An investigation of the population parameters of Indian mackerel, Rastrelliger kanagurta (Cuvier, 1816) in the Marudu Bay, Sabah, Malaysia was carried out from January to September 2013. The relationship between total length and body weight was estimated as W=0.006TL3.215 or Log W=3.215LogTL – 2.22 (R2=0.946). Monthly length frequency data of R. kanagurta were analyzed by FiSAT software to eva...

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e. AC tampering functions), our codes have codeword length n = k for a k-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay and Li (STOC 2017), which had codew...

Regular expression matching is a key task (and often the computational bottleneck) in a variety of widely used software tools and applications, for instance, the unix grep and sed commands, scripting languages such as awk and perl, programs for analyzing massive data streams, etc. We show how to solve this ubiquitous task in linear space and O(nm(log log n)/(log n)+n+m) time where m is the leng...