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We consider the problem of finding a minimum common partition of two strings (MCSP). The problem has its application in genome comparison. MCSP problem is proved to be NP-hard. In this paper, we develop an Integer Programming (IP)…
The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover,…
In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial…
Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is 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…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
The NP-hard Minimum Common String Partition problem asks whether two strings $x$ and $y$ can each be partitioned into at most $k$ substrings, called blocks, such that both partitions use exactly the same blocks in a different order. We…
The Multi-Criteria Test Suite Minimization (MCTSM) problem aims to remove redundant test cases, guided by adequacy criteria such as code coverage or fault detection capability. However, current techniques either exhibit a high loss of fault…