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We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…
Canonical polyadic decomposition (CPD) is at the core of fast matrix multiplication, a computational problem with widespread implications across several seemingly unrelated problems in computer science. Much recent progress in this field…
Despite a surge of interest in submodular maximization in the data stream model, there remain significant gaps in our knowledge about what can be achieved in this setting, especially when dealing with multiple constraints. In this work, we…
Multi-Agent Path Finding (MAPF) is a challenging combinatorial problem that asks us to plan collision-free paths for a team of cooperative agents. In this work, we show that one of the reasons why MAPF is so hard to solve is due to a…
One of the most important questions in matroid optimization is to find disjoint common bases of two matroids. The significance of the problem is well-illustrated by the long list of conjectures that can be formulated as special cases.…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
The concept of space-bounded computability has become significantly important in handling vast data sets on memory-limited computing devices. To replenish the existing short list of NL-complete problems whose instance sizes are dictated by…
Machine learning (ML) algorithms are predictively competitive algorithms with many human-impact applications. However, the issue of long execution time remains unsolved in the literature for high-dimensional spaces. This study proposes…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
The problem of scheduling conflicting jobs on parallel machines consists in assigning a set of jobs to a set of machines so that no two conflicting jobs are allocated to the same machine, and the maximum processing time among all machines…
We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph $G= (A \cup P, E)$ with weights on the edges in $E$, and with lower and upper quotas on the vertices in $P$. We…
In the Inverse Matroid problem, we are given a matroid, a fixed basis $B$, and an initial weight function, and the goal is to minimally modify the weights -- measured by some function -- so that $B$ becomes a maximum-weight basis. The…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
This research investigates a multi-product capacitated lot-sizing and scheduling problem incorporating a novel learning effect, namely the period-based learning effect. This is inspired by a real case in a core analysis laboratory under a…
In the matroid intersection problem, we are given two matroids $\mathcal{M}_1 = (V, \mathcal{I}_1)$ and $\mathcal{M}_2 = (V, \mathcal{I}_2)$ defined on the same ground set $V$ of $n$ elements, and the objective is to find a common…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
This paper studies randomized polynomial kernelization for the weighted $d$-matroid intersection problem. While the problem is known to have a kernel of size $O(d^{(k - 1)d})$ where $k$ is the solution size, the existence of a polynomial…
This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set $E$ and $k$ weighted matroids $(E, \mathcal{I}_i, w_i)$, $i = 1, \dots, k$, and our task is to find a…
Condensed Matter Physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many…