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We consider the problem of computing optimal search trees on trees (STTs). STTs generalize binary search trees (BSTs) in which we search nodes in a path (linear order) to search trees that facilitate search over general tree topologies.…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
This paper studies strategies to optimize the lane configuration of a transportation network for a given set of Origin-Destination demands using a planning macroscopic network flow model. The lane reversal problem is, in general, NP-hard…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
The deployment of large language models (LLMs) is often constrained by their substantial computational and memory demands. While structured pruning presents a viable approach by eliminating entire network components, existing methods suffer…
The performance of distributed and data-centric applications often critically depends on the interconnecting network. Applications are hence modeled as virtual networks, also accounting for resource demands on links. At the heart of…
Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…
This work considers the path planning problem for a team of identical robots evolving in a known environment. The robots should satisfy a global specification given as a Linear Temporal Logic (LTL) formula over a set of regions of interest.…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
Given a tree, a set of pebbles initially stationed at some nodes of the tree, and a set of target nodes, the Unlabeled Pebble Motion on Trees problem (UPMT) asks to find a plan to move the pebbles one-at-a-time from the starting nodes to…
In this paper we present and evaluate a parallel algorithm for solving a minimum spanning tree (MST) problem for supercomputers with distributed memory. The algorithm relies on the relaxation of the message processing order requirement for…
Considering an environment containing polygonal obstacles, we address the problem of planning motions for a pair of planar robots connected to one another via a cable of limited length. Much like prior problems with a single robot connected…
Recently, Internet service providers (ISPs) have gained increased flexibility in how they configure their in-ground optical fiber into an IP network. This greater control has been made possible by (i) the maturation of software defined…
The problem considered is the following. Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified…
Discrete Optimal Transport problems give rise to very large linear programs (LP) with a particular structure of the constraint matrix. In this paper we present a hybrid algorithm that mixes an interior point method (IPM) and column…
For a given graph $G=(V,\, E)$ with a terminal set $S$ and a selected root $r\in S$, a positive integer cost and a delay on every edge and a delay constraint $D\in Z^{+}$, the shallow-light Steiner tree (\emph{SLST}) problem is to compute a…
This paper studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e.,…
Designing cable harnesses can be time-consuming and complex due to many design and manufacturing aspects and rules. Automating the design process can help to fulfil these rules, speed up the process, and optimize the design. To accommodate…