Related papers: Optimal Tree Topology for a Submarine Cable Networ…
We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci.,…
We study the problem of solving linear program in the streaming model. Given a constraint matrix $A\in \mathbb{R}^{m\times n}$ and vectors $b\in \mathbb{R}^m, c\in \mathbb{R}^n$, we develop a space-efficient interior point method that…
Cable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic…
This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterative method for doing so in 3D space. Such a network will be…
We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
Our motivation is to improve on the best approximation guarantee known for the problem of finding a minimum-cost 2-node connected spanning subgraph of a given undirected graph with nonnegative edge costs. We present an LP (Linear…
We investigate the task and motion planning problem for Signal Temporal Logic (STL) specifications in robotics. Existing STL methods rely on pre-defined maps or mobility representations, which are ineffective in unstructured real-world…
In the Tree Augmentation Problem (TAP) the goal is to augment a tree $T$ by a minimum size edge set $F$ from a given edge set $E$ such that $T \cup F$ is $2$-edge-connected. The best approximation ratio known for TAP is $1.5$. In the more…
Planning under resource constraints is central to real-world decision making, yet most large language model (LLM) planners assume uniform action costs. We systematically analyze whether tree-search LLM planners are cost-aware and whether…
In this chapter, an integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, environment abstractions for resource-constrained autonomous agents is presented. The formulation leverages concepts…
We consider unreliable multi-hop networks serving multiple flows in which packets not delivered to their destination nodes by their deadlines are dropped. We address the design of policies for routing and scheduling packets that optimize…
Inspired by sled-pulling dogs in transportation, we present a cable-trailer integrated with a quadruped robot system. The motion planning of this system faces challenges due to the interactions between the cable's state transitions, the…
In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests…
We propose a novel, multi-layered planning approach for computing paths that satisfy both kinodynamic and spatiotemporal constraints. Our three-part framework first establishes potential sequences to meet spatial constraints, using them to…
There exist many criteria for the optimal design of water distribution networks. One of the most common criteria is to design the optimal cost water distribution network while satisfying the hydraulic design constraints. This study was…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…