arXiv subjects

Kevin Hsu

Publications and source records attributed to Kevin Hsu.

9 recordsLinked to original sources

arXiv2025

Fair Division of Indivisible Items

We study the fair division of indivisible items. In the general model, the goal is to allocate $m$ indivisible items to $n$ agents while satisfying fairness criteria such as MMS, EF1, and EFX. We also study a recently-introduced graphical model that represents the fair division problem as a multigraph, in which vertices correspond to agents and edges to items. The graphical model stipulates that an item can have non-zero marginal utility to an agent only if its corresponding edge is incident to the agent's corresponding vertex. We study orientations (allocations that allocate each edge to an endpoint) in this model, as they are particularly desirable. Our first contribution concerns MMS allocations of mixed manna (i.e. a mixture of goods and chores) in the general model. It is known that MMS allocations of goods exist when $m \leq n+5$. We generalize this and show that when $m \leq n+5$, MMS allocations of mixed manna exist as long as $n \leq 3$, there is an agent whose MMS threshold is non-negative, or every item is a chore. Remarkably, our result leaves only the case where every agent has a negative MMS threshold unanswered. Our second contribution concerns EFX orientations of multigraphs of goods. We show that deciding whether EFX orientations exist for multigraphs is NP-complete, even for symmetric bi-valued multigraphs. Complementarily, we show symmetric bi-valued multigraphs that do not contain non-trivial odd multitrees have EFX orientations that can be found in polynomial time. Our third contribution concerns EF1 and EFX orientations of graphs and multigraphs of chores. We obtain polynomial-time algorithms for deciding whether such graphs have EF1 and EFX orientations, resolving a previous conjecture and showing a fundamental difference between goods and chores division. In addition, we show that the analogous problems for multigraphs are NP-hard.

cs.GT↗

arXiv2025

InfoVids: Reimagining the Viewer Experience with Alternative Visualization-Presenter Relationships

Traditional data presentations typically separate the presenter and visualization into two separate spaces--the 3D world and a 2D screen--enforcing visualization-centric stories. To create a more human-centric viewing experience, we establish a more equitable relationship between the visualization and the presenter through our InfoVids. These infographics-inspired informational videos are crafted to redefine relationships between the presenter and visualizations. As we design InfoVids, we explore how the use of layout, form, and interactions affects the viewer experience. We compare InfoVids against their baseline 2D `slides' equivalents across 9 metrics with 30 participants and provide practical, long-term insights from an autobiographical perspective. Our mixed methods analyses reveal that this paradigm reduced viewer attention splitting, shifted the focus from the visualization to the presenter, and led to more interactive, natural, and engaging full-body data performances for viewers. Ultimately, InfoVids helped viewers re-imagine traditional dynamics between the presenter and visualizations.

cs.HC↗

arXiv2025

Polynomial-Time Algorithms for Fair Orientations of Chores

This paper addresses the problem of finding fair orientations of graphs of chores, in which each vertex corresponds to an agent, each edge corresponds to a chore, and a chore has zero marginal utility to an agent if its corresponding edge is not incident to the vertex corresponding to the agent. Recently, Zhou et al. (IJCAI, 2024) analyzed the complexity of deciding whether graphs containing a mixture of goods and chores have EFX orientations, and conjectured that deciding whether graphs containing only chores have EFX orientations is NP-complete. We resolve this conjecture by giving polynomial-time algorithms that find EF1 and EFX orientations of graphs containing only chores if they exist, even if there are self-loops. Remarkably, our result demonstrates a surprising separation between the case of goods and the case of chores, because deciding whether graphs containing only goods have EFX orientations was shown to be NP-complete by Christodoulou et al. (EC, 2023). In addition, we show the EF1 and EFX orientation problems for multigraphs to be NP-complete.

cs.GT↗

arXiv2024

EFX Orientations of Multigraphs

We study EFX orientations of multigraphs with self-loops. In this setting, vertices represent agents, edges represent goods, and a good provides positive utility to an agent only if it is incident to the agent. We focus on the bi-valued symmetric case in which each edge has equal utility to both incident agents, and edges have one of two possible utilities $\alpha > \beta \geq 0$. In contrast with the case of simple graphs for which bipartiteness implies the existence of an EFX orientation, we show that deciding whether a symmetric multigraph $G$ of any multiplicity $q \geq 2$ has an EFX orientation is NP-complete even if $G$ is bipartite, $\alpha > q\beta$, and $G$ contains a structure called a non-trivial odd multitree (NTOM). Moreover, we show that NTOMs are a problematic structure in the sense that even very simple NTOMs can fail to have EFX orientations, and multigraphs that do not contain NTOMs always have EFX orientations that can be found in polynomial-time.

cs.GT↗

arXiv2024

Hierarchical Large Scale Multirobot Path (Re)Planning

We consider a large-scale multi-robot path planning problem in a cluttered environment. Our approach achieves real-time replanning by dividing the workspace into cells and utilizing a hierarchical planner. Specifically, we propose novel multi-commodity flow-based high-level planners that route robots through cells with reduced congestion, along with an anytime low-level planner that computes collision-free paths for robots within each cell in parallel. A highlight of our method is a significant improvement in computation time. Specifically, we show empirical results of a 500-times speedup in computation time compared to the baseline multi-agent pathfinding approach on the environments we study. We account for the robot's embodiment and support non-stop execution with continuous replanning. We demonstrate the real-time performance of our algorithm with up to 142 robots in simulation, and a representative 32 physical Crazyflie nano-quadrotor experiment.

cs.RO↗

arXiv2024

Existence of MMS Allocations with Mixed Manna

Maximin share (MMS) allocations are a popular relaxation of envy-free allocations that have received wide attention in the fair division of indivisible items. Although MMS allocations of goods can fail to exist, previous work has found conditions under which they exist. Specifically, MMS allocations of goods exist whenever $m \leq n+5$, and this bound is tight in the sense that they can fail to exist when $m = n+6$. The techniques used to obtain these results do not apply to the mixed manna setting, leaving the question of whether similar results hold for the general setting. This paper addresses this by introducing new techniques to handle these settings. In particular, we are able to answer this question completely for the chores setting, and partially for the mixed manna setting. An agent $i$ is a {\em chores agent} if it considers every item to be a chore and a {\em non-negative agent} if its MMS guarantee is non-negative. In this paper, we prove that an MMS allocation exists as long as $m \leq n+5$ and either (i) every agent is a chores agent, or (ii) there exists a non-negative agent. In addition, for $n \leq 3$, we also prove that an MMS allocation exists as long as $m \leq n+5$, regardless of the types of agents. To the best of our knowledge, these are the first non-trivial results pertaining to the existence of exact MMS allocations in the mixed manna setting.

cs.GT↗

arXiv2022

An Improved Lower Bound for Maximin Share Allocations of Goods

The problem of fair division of indivisible goods has been receiving much attention recently. The prominent metric of envy-freeness can always be satisfied in the divisible goods setting (see for example \cite{BT95}), but often cannot be satisfied in the indivisible goods setting. This has led to many relaxations thereof being introduced. We study the existence of {\em maximin share (MMS)} allocations, which is one such relaxation. Previous work has shown that MMS allocations are guaranteed to exist for all instances with $n$ players and $m$ goods if $m \leq n+4$. We extend this guarantee to the case of $m = n+5$ and show that the same guarantee fails for $m = n+6$.

cs.GT↗

arXiv2021

Obstructions for local tournament orientation completions

The orientation completion problem for a class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class by orienting the unoriented edges of the partially oriented graph. Orientation completion problems have been studied recently for several classes of oriented graphs, yielding both polynomial time solutions as well as NP-completeness results. Local tournaments are a well-structured class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. According to Skrien, a connected graph can be oriented as a local tournament if and only if it is a proper circular-arc graph. Proper interval graphs are precisely the graphs which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for the classes of local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we characterize the partially oriented graphs that can be completed to local tournaments by determining the complete list of obstructions. These are in a sense minimal partially oriented graphs that cannot be completed to local tournaments. The result may be viewed as an extension of the well-known forbidden subgraph characterization of proper circular-arc graphs obtained by Tucker. The complete list of obstructions for acyclic local tournament orientation completions has been given in a companion paper.

math.CO↗

arXiv2020

Obstructions for acyclic local tournament orientation completions

The orientation completion problem for a fixed class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class. Orientation completion problems have been studied recently for several classes of oriented graphs, yielding both polynomial time solutions and NP-completeness results. Local tournaments are a well-structured class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. Proper interval graphs are precisely those which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we identify the obstructions for acyclic local tournament orientation completions. These are in a sense minimal partially oriented graphs that cannot be completed to acyclic local tournaments. Our description of the obstructions imply that they can be recognized in polynomial time. In a companion paper we will determine all obstructions for local tournament orientation completions.

math.CO↗