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A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
Recently, the predicate detection problem was shown to be in the parallel complexity class NC. In this paper, we give the first work-optimal parallel algorithm to solve the predicate detection problem on a distributed computation with $n$…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
This work proposes an efficient parallel algorithm for non-monotone submodular maximization under a knapsack constraint problem over the ground set of size $n$. Our algorithm improves the best approximation factor of the existing parallel…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
In this paper we address the constrained longest common subsequence problem. Given two sequences $X$, $Y$ and a constrained sequence $P$, a sequence $Z$ is a constrained longest common subsequence for $X$ and $Y$ with respect to $P$ if $Z$…
Magnetic tapes have been playing a key role as means for storage of digital data for decades, and their unsurpassed cost-effectiveness still make them the technology of choice in several industries, such as media and entertainment. Tapes…
In this paper, we consider a generalized longest common subsequence problem with multiple substring inclusive constraints. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints $P=\{P_1,\cdots,P_d\}$…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
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…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…
Given two sequences $A[1..n]$ and $B[1..m]$ over a totally ordered alphabet, the \emph{Longest Common Bitonic Subsequence} (LCBS) problem asks for a longest common subsequence that is strictly increasing up to a single peak element and…