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We address the following general question: given a graph class C on which we can solve Maximum Matching in (quasi) linear time, does the same hold true for the class of graphs that can be modularly decomposed into C ? A major difficulty in…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
We study the Lattice Isomorphism Problem (LIP), in which given two lattices L_1 and L_2 the goal is to decide whether there exists an orthogonal linear transformation mapping L_1 to L_2. Our main result is an algorithm for this problem…
This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems,…
Cooperative driving at signal-free intersections, which aims to improve driving safety and efficiency for connected and automated vehicles, has attracted increasing interest in recent years. However, existing cooperative driving strategies…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
The Maximum Clique Problem (MCP) is a foundational NP-hard problem with wide-ranging applications, yet no single algorithm consistently outperforms all others across diverse graph instances. This underscores the critical need for…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
We introduce a class of concurrent learning (CL) algorithms designed to solve parameter estimation problems with convergence rates ranging from hyperexponential to prescribed-time while utilizing alternating datasets during the learning…
The shortest bibranching problem is a common generalization of the minimum-weight edge cover problem in bipartite graphs and the minimum-weight arborescence problem in directed graphs. For the shortest bibranching problem, an efficient…
One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity…
A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in…
Multirobot systems for covering environments are increasingly used in applications like cleaning, industrial inspection, patrolling, and precision agriculture. The problem of covering a given environment using multiple robots can be…
Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P,…
The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…
Let $M$ be a matroid defined on a finite set $E$ and $L\subset E$. $L$ is locked in $M$ if $M|L$ and $M^*|(E\backslash L)$ are 2-connected, and $min\{r(L), r^*(E\backslash L)\} \geq 2$. Locked subsets characterize nontrivial facets of the…
We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $\mathcal{NP}$-complete…
Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…
Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…