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We study the classic subgraph enumeration problem under distributed settings. Existing solutions either suffer from severe memory crisis or rely on large indexes, which makes them impractical for very large graphs. Most of them follow a…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
We address a fundamental problem arising from analysis of biomolecular sequences. The input consists of two numbers $w_{\min}$ and $w_{\max}$ and a sequence $S$ of $n$ number pairs $(a_i,w_i)$ with $w_i>0$. Let {\em segment} $S(i,j)$ of $S$…
Let $A$ and $B$ be two number sequences of length $n$ and $m$, respectively, where $m\le n$. Given a positive number $\delta$, a common almost increasing sequence $s_1\ldots s_k$ is a common subsequence for both $A$ and $B$ such that for…
In this paper, we study for the first time the Diverse Longest Common Subsequences (LCSs) problem under Hamming distance. Given a set of a constant number of input strings, the problem asks to decide if there exists some subset $\mathcal X$…
We revisit the exact shortest unique substring (SUS) finding problem, and propose its approximate version where mismatches are allowed, due to its applications in subfields such as computational biology. We design a generic in-place…
A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from…
The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant…
In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a constraint string $P$ of length $r$, the…
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…
We consider the complexity for computing the approximate sum $a_1+a_2+...+a_n$ of a sorted list of numbers $a_1\le a_2\le ...\le a_n$. We show an algorithm that computes an $(1+\epsilon)$-approximation for the sum of a sorted list of…
Given an array A of n real numbers, the maximum subarray problem is to find a contiguous subarray which has the largest sum. The k-maximum subarrays problem is to find k such subarrays with the largest sums. For the 1-maximum subarray the…
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
Given $N$ instances $(X_1,t_1),\ldots,(X_N,t_N)$ of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers $X_i$ has a subset that sums up to the…
In this paper, we revisit the much studied LCS problem for two given sequences. Based on the algorithm of Iliopoulos and Rahman for solving the LCS problem, we have suggested 3 new improved algorithms. We first reformulate the problem in a…
In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for…
In recent years we have witnessed an increase on the development of methods for submodular optimization, which have been motivated by the wide applicability of submodular functions in real-world data-science problems. In this paper, we…
Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…
In this paper, we investigate the complexity of one-dimensional dynamic programming, or more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of $n$ data items together with weights for every pair of the items,…