Related papers: A Simple Algorithm for the Constrained Sequence Pr…
Given a text $T$ and a pattern $P$, the order-preserving matching problem is to find all substrings in $T$ which have the same relative orders as $P$. Order-preserving matching has been an active research area since it was introduced by…
The $k$-mismatch problem consists in computing the Hamming distance between a pattern $P$ of length $m$ and every length-$m$ substring of a text $T$ of length $n$, if this distance is no more than $k$. In many real-world applications, any…
Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…
The problem of scheduling under resource constraints is widely applicable. One prominent example is power management, in which we have a limited continuous supply of power but must schedule a number of power-consuming tasks. Such problems…
A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…
A pangenome captures the genetic diversity across multiple individuals simultaneously, providing a more comprehensive reference for genome analysis than a single linear genome, which may introduce allele bias. A widely adopted pangenome…
Given a sequence of n numbers, the Maximum Consecutive Subsums Problem (MCSP) asks for the maximum consecutive sum of lengths l for each l = 1,...,n. No algorithm is known for this problem which is significantly better than the naive…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
In the area of Pattern Recognition and Matching, finding a Longest Common Subsequence plays an important role. In this paper, we have proposed one algorithm based on parallel computation. We have used OpenMP API package as middleware to…
Given a text and a pattern over an alphabet, the pattern matching problem searches for all occurrences of the pattern in the text. An equivalence relation $\approx$ is called a substring consistent equivalence relation (SCER), if for two…
Partitioning a sequence of length $n$ into $k$ coherent segments (Seg) is one of the classic optimization problems. As long as the optimization criterion is additive, Seg can be solved exactly in $O(n^2k)$ time using a classic dynamic…
Given a set $P$ of $n$ points and a set $S$ of $n$ segments in the plane, we consider the problem of computing for each segment of $S$ its closest point in $P$. The previously best algorithm solves the problem in $n^{4/3}2^{O(\log^*n)}$…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…
The problem of finding longest common subsequence (LCS) is one of the fundamental problems in computer science, which finds application in fields such as computational biology, text processing, information retrieval, data compression etc.…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…
Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…
For a string $S$, a palindromic substring $S[i..j]$ is said to be a \emph{shortest unique palindromic substring} ($\mathit{SUPS}$) for an interval $[s, t]$ in $S$, if $S[i..j]$ occurs exactly once in $S$, the interval $[i, j]$ contains $[s,…
Let us consider the Multiple String Matching Problem. In this problem, we consider a long string, denoted by $t$, of length $n$. This string is referred to as a text. We also consider a sequence of $m$ strings, denoted by $S$, which we…