arXiv subjects

Young-San Lin

Publications and source records attributed to Young-San Lin.

14 recordsLinked to original sources

arXiv2026

Estimation, Prediction, and Assortment Optimization for Markov Chain Choice Models with Panel Data

We propose a framework for the Markov chain (MC) choice model with panel data, including parameter estimation, personalized choice prediction, and personalized assortment optimization. In contrast to the traditional setting, which assumes that each transaction is independently drawn from a random utility model, our framework accounts for dependencies among transactions for the same customer in historical data, captured by partial-ordering preference information. To the best of our knowledge, our framework initiates the study of choice modeling with panel data under MC. As our primary result, we propose novel expectation-maximization (EM) algorithms for MC parameter estimation by incorporating partial-ordering-based customer preference information. On synthetic datasets and the sushi dataset, our EM algorithms outperform the traditional EM algorithm of Simsek and Topaloglu (Operations Research, 66, 2018) and multinomial-logit-based partial-order benchmarks adapted from Jagabathula and Vulcano (Management Science, 64, 2018). As our secondary contribution, we present hardness and computational results for conditional choice prediction and assortment optimization problems. These results complement our estimation framework and clarify the computational landscape of conditional choice and assortment optimization, which may be of independent interest.

cs.LG↗

arXiv2025

Improved and Parameterized Algorithms for Online Multi-level Aggregation: A Memory-based Approach

We study the online multi-level aggregation problem with deadlines (MLAP-D) introduced by Bienkowski et al. (ESA 2016, OR 2020). In this problem, requests arrive over time at the vertices of a given vertex-weighted tree, and each request has a deadline that it must be served by. The cost of serving a request equals the cost of a path from the root to the vertex where the request resides. Instead of serving each request individually, requests can be aggregated and served by transmitting a subtree from the root that spans the vertices on which the requests reside, to potentially be more cost-effective. The aggregated cost is the weight of the transmission subtree. The goal of MLAP-D is to find an aggregation solution that minimizes the total cost while serving all requests. We present improved and parameterized algorithms for MLAP-D. Our result is twofold. First, we present an $e(D+1)$-competitive algorithm where $D$ is the depth of the tree. Second, we present an $e(4H+2)$-competitive algorithm where $H$ is the caterpillar dimension of the tree. Here, $H \le D$ and $H \le \log_2 |V|$ where $|V|$ is the number of vertices in the given tree. The caterpillar dimension remains constant for rich but simple classes of trees, such as line graphs ($H=1$), caterpillar graphs ($H=2$), and lobster graphs ($H=3$). To the best of our knowledge, this is the first online algorithm parameterized on a measure better than depth. The state-of-the-art online algorithms are $6(D+1)$-competitive by Buchbinder, Feldman, Naor, and Talmon (SODA 2017) and $O(\log |V|)$-competitive by Azar and Touitou (FOCS 2020). Our framework outperforms the state-of-the-art ratios when $H = o(\min\{D,\log_2 |V|\})$. Our simple framework directly applies to trees with any structure and differs from the previous frameworks that reduce the problem to trees with specific structures.

cs.DS↗

arXiv2025

A few good choices

A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to $\alpha$-undominated sets, which ensure the same property for any $\alpha$-fraction of voters and are guaranteed to exist in constant size for any $\alpha$. However, the requirement that an outsider be preferred to every member of the set can be overly restrictive and difficult to justify in many applications. Motivated by this, we introduce a more flexible notion: $(t, \alpha)$-undominated sets. Here, each voter compares an outsider to their $t$-th most preferred member of the set, and the set is undominated if no outsider is preferred by more than an $\alpha$-fraction of voters. This framework subsumes prior definitions, recovering Condorcet winning sets when $(t = 1, \alpha = 1/2)$ and $\alpha$-undominated sets when $t = 1$, and introduces a new, tunable notion of collective acceptability for $t > 1$. We establish three main results: 1. We prove that a $(t, \alpha)$-undominated set of size $O(t/\alpha)$ exists for all values of $t$ and $\alpha$. 2. We show that as $t$ becomes large, the minimum size of such a set approaches $t/\alpha$, which is asymptotically optimal. 3. In the special case $t = 1$, we improve the bound on the size of an $\alpha$-undominated set given by Charikar, Lassota, Ramakrishnan, Vetta, and Wang (STOC 2025). As a consequence, we show that a Condorcet winning set of five candidates exists, improving their bound of six.

cs.GT↗

arXiv2024

Routing-Controlled Spanners

Designing sparse directed spanners, which are subgraphs that approximately maintain distance constraints, has attracted sustained interest in TCS, especially due to their wide applicability, as well as the difficulty to obtain tight results. However, a significant drawback of the notion of spanners is that it does not capture a natural setting where demand pairs are subject to restrictions beyond a distance constraint. In this paper we initiate the study of **routing-controlled spanners**, where in addition to distance constraints, demand pairs are also subjected to routing constraints, which may require or forbid visiting specific vertices on feasible paths. The goal is to find a minimum-cost routing solution that satisfies the multiple constraints. Moreover, we introduce an even more general notion, which we call **packing-covering spanner**, where each demand pair is subjected to a number of packing and covering constraints, in addition to a distance constraint. Packing-covering spanners capture other natural network connectivity problems such as optimal hopsets and graph spanners for group Steiner distances. To the best of our knowledge, we obtain the first approximation algorithms for the packing-covering spanner problem, and thus for the routing-controlled spanners, under natural assumptions. Our results match the state-of-the-art approximation ratios in special cases of ours, such as Steiner Forests and Directed Spanners. Our results also imply approximation algorithms for optimal hopsets and graph spanners for group Steiner distances in the directed setting, and position packing-covering spanners as a natural abstraction unifying several well-studied problems in directed network design.

cs.DS↗

arXiv2024

Learning-Augmented Algorithms for Online Concave Packing and Convex Covering Problems

Learning-augmented algorithms have been extensively studied across the computer science community in the recent years, driven by advances in machine learning predictors, which can provide additional information to augment classical algorithms. Such predictions are especially powerful in the context of online problems, where decisions have to be made without knowledge of the future, and which traditionally exhibits impossibility results bounding the performance of any online algorithm. The study of learning-augmented algorithms thus aims to use external advice prudently, to overcome classical impossibility results when the advice is accurate, and still perform comparably to the state-of-the-art online algorithms even when the advice is inaccurate. In this paper, we present learning-augmented algorithmic frameworks for two fundamental optimizations settings, extending and generalizing prior works. For online packing with concave objectives, we present a simple but overarching strategy that switches between the advice and the state-of-the-art online algorithm. For online covering with convex objectives, we greatly extend primal-dual methods for online convex covering programs by Azar et al. (FOCS 2016) and previous learning-augmented framework for online covering linear programs from the literature, to many new applications. We show that our algorithms break impossibility results when the advice is accurate, while maintaining comparable performance with state-of-the-art classical online algorithms even when the advice is erroneous.

cs.DS↗

arXiv2024

A Simple Learning-Augmented Algorithm for Online Packing with Concave Objectives

Learning-augmented algorithms has been extensively studied recently in the computer-science community, due to the potential of using machine learning predictions in order to improve the performance of algorithms. Predictions are especially useful for online algorithms making irrevocable decisions without knowledge of the future. Such learning-augmented algorithms aim to overcome the limitations of classical online algorithms when the predictions are accurate, and still perform comparably when the predictions are inaccurate. A common approach is to adapt existing online algorithms to the particular advice notion employed, which often involves understanding previous sophisticated algorithms and their analyses. However, ideally, one would simply use previous online solutions in a black-box fashion, without much loss in the approximation guarantees. Such clean solutions that avoid opening up black-boxes are often rare, and may be even missed the first time around. For example, Grigorescu et al. (NeurIPS 22) proposed a learning-augmented algorithms for online covering linear programs, but it later turned out that their results can be subsumed by a natural approach that switches between the advice and an online algorithm given as a black-box, as noted in their paper. In this work, we introduce and analyze a simple learning-augmented algorithm for online packing problems with linear constraints and concave objectives. We exhibit several direct applications of our framework including online packing linear programming, knapsack, resource management benefit, throughput maximization, and network utility maximization. We further raise the problem of understanding necessary and sufficient conditions for when such simple black-box solutions may be optimal. We believe this is an important direction of research that would unify many ad-hoc approaches from the literature.

cs.DS↗

arXiv2024

Directed Buy-at-Bulk Spanners

We present a framework that unifies directed buy-at-bulk network design and directed spanner problems, namely, buy-at-bulk spanners. The goal is to find a minimum-cost routing solution for network design problems that capture economies at scale, while satisfying demands and distance constraints for terminal pairs. A more restricted version of this problem was shown to be $O(2^{{\log^{1-\varepsilon} n}})$-hard to approximate, where $n$ is the number of vertices, under a standard complexity assumption, due to Elkin and Peleg (Theory of Computing Systems, 2007). To the best of our knowledge, our results are the first sublinear factor approximation algorithms for directed buy-at-bulk spanners. Furthermore, these results hold even when we allow the edge lengths to be negative, unlike the previous literature for spanners. Our approximation ratios match the state-of-the-art ratios in special cases, namely, buy-at-bulk network design by Antonakopoulos (WAOA, 2010) and weighted spanners by Grigorescu, Kumar, and Lin (APPROX 2023). Our results are based on new approximation algorithms for the following two problems that are of independent interest: minimum-density distance-constrained junction trees and resource-constrained shortest path with negative consumption.

cs.DS↗

arXiv2023

Approximation Algorithms for Directed Weighted Spanners

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a minimum-cost subgraph in which the distance constraints are satisfied. This formulation captures many well-studied connectivity problems, including spanners, distance preservers, and Steiner forests. In the offline setting, we show: 1. An $\tilde{O}(n^{4/5 + ε})$-approximation algorithm for pairwise weighted spanners. When the edges have unit costs and lengths, the best previous algorithm gives an $\tilde{O}(n^{3/5 + ε})$-approximation, due to Chlamtáč, Dinitz, Kortsarz, and Laekhanukit (TALG, 2020). 2. An $\tilde{O}(n^{1/2+ε})$-approximation algorithm for all-pair weighted distance preservers. When the edges have unit costs and arbitrary lengths, the best previous algorithm gives an $\tilde{O}(n^{1/2})$-approximation for all-pair spanners, due to Berman, Bhattacharyya, Makarychev, Raskhodnikova, and Yaroslavtsev (Information and Computation, 2013). In the online setting, we show: 1. An $\tilde{O}(k^{1/2 + ε})$-competitive algorithm for pairwise weighted spanners. The state-of-the-art results are $\tilde{O}(n^{4/5})$-competitive when edges have unit costs and arbitrary lengths, and $\min\{\tilde{O}(k^{1/2 + ε}), \tilde{O}(n^{2/3 + ε})\}$-competitive when edges have unit costs and lengths, due to Grigorescu, Lin, and Quanrud (APPROX, 2021). 2. An $\tilde{O}(k^ε)$-competitive algorithm for single-source weighted spanners. Without distance constraints, this problem is equivalent to the directed Steiner tree problem. The best previous algorithm for online directed Steiner trees is $\tilde{O}(k^ε)$-competitive, due to Chakrabarty, Ene, Krishnaswamy, and Panigrahi (SICOMP, 2018).

cs.DS↗

arXiv2023

Online Directed Spanners and Steiner Forests

We present online algorithms for directed spanners and Steiner forests. These problems fall under the unifying framework of online covering linear programming formulations, developed by Buchbinder and Naor (MOR, 34, 2009), based on primal-dual techniques. Our results include the following: For the pairwise spanner problem, in which the pairs of vertices to be spanned arrive online, we present an efficient randomized $\tilde{O}(n^{4/5})$-competitive algorithm for graphs with general lengths, where $n$ is the number of vertices. With uniform lengths, we give an efficient randomized $\tilde{O}(n^{2/3+ε})$-competitive algorithm, and an efficient deterministic $\tilde{O}(k^{1/2+ε})$-competitive algorithm, where $k$ is the number of terminal pairs. These are the first online algorithms for directed spanners. In the offline setting, the current best approximation ratio with uniform lengths is $\tilde{O}(n^{3/5 + ε})$, due to Chlamtac, Dinitz, Kortsarz, and Laekhanukit (TALG 2020). For the directed Steiner forest problem with uniform costs, in which the pairs of vertices to be connected arrive online, we present an efficient randomized $\tilde{O}(n^{2/3 + ε})$-competitive algorithm. The state-of-the-art online algorithm for general costs is due to Chakrabarty, Ene, Krishnaswamy, and Panigrahi (SICOMP 2018) and is $\tilde{O}(k^{1/2 + ε})$-competitive. In the offline version, the current best approximation ratio with uniform costs is $\tilde{O}(n^{4/7 + ε})$, due to Abboud and Bodwin (SODA 2018). A small modification of the online covering framework by Buchbinder and Naor implies a polynomial-time primal-dual approach with separation oracles, which a priori might perform exponentially many calls. We convert the online spanner problem and the online Steiner forest problem into online covering problems and round in a problem-specific fashion.

cs.DS↗

arXiv2022

Learning-Augmented Algorithms for Online Linear and Semidefinite Programming

Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist known impossibility results for approximating the optimal solution when constraints for covering SDPs arrive in an online fashion. In this paper, we study online covering linear and semidefinite programs in which the algorithm is augmented with advice from a possibly erroneous predictor. We show that if the predictor is accurate, we can efficiently bypass these impossibility results and achieve a constant-factor approximation to the optimal solution, i.e., consistency. On the other hand, if the predictor is inaccurate, under some technical conditions, we achieve results that match both the classical optimal upper bounds and the tight lower bounds up to constant factors, i.e., robustness. More broadly, we introduce a framework that extends both (1) the online set cover problem augmented with machine-learning predictors, studied by Bamas, Maggiori, and Svensson (NeurIPS 2020), and (2) the online covering SDP problem, initiated by Elad, Kale, and Naor (ICALP 2016). Specifically, we obtain general online learning-augmented algorithms for covering linear programs with fractional advice and constraints, and initiate the study of learning-augmented algorithms for covering SDP problems. Our techniques are based on the primal-dual framework of Buchbinder and Naor (Mathematics of Operations Research, 34, 2009) and can be further adjusted to handle constraints where the variables lie in a bounded region, i.e., box constraints.

cs.DS↗

arXiv2021

Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree

A heapable sequence is a sequence of numbers that can be arranged in a "min-heap data structure". Finding a longest heapable subsequence of a given sequence was proposed by Byers, Heeringa, Mitzenmacher, and Zervas (ANALCO 2011) as a generalization of the well-studied longest increasing subsequence problem and its complexity still remains open. An equivalent formulation of the longest heapable subsequence problem is that of finding a maximum-sized binary tree in a given permutation directed acyclic graph (permutation DAG). In this work, we study parameterized algorithms for both longest heapable subsequence as well as maximum-sized binary tree. We show the following results: 1. The longest heapable subsequence problem can be solved in $k^{O(\log{k})}n$ time, where $k$ is the number of distinct values in the input sequence. We introduce the "alphabet size" as a new parameter in the study of computational problems in permutation DAGs. Our result on longest heapable subsequence implies that the maximum-sized binary tree problem in a given permutation DAG is fixed-parameter tractable when parameterized by the alphabet size. 2. We show that the alphabet size with respect to a fixed topological ordering can be computed in polynomial time, admits a min-max relation, and has a polyhedral description. 3. We design a fixed-parameter algorithm with run-time $w^{O(w)}n$ for the maximum-sized binary tree problem in undirected graphs when parameterized by treewidth $w$. Our results make progress towards understanding the complexity of the longest heapable subsequence and maximum-sized binary tree in permutation DAGs from the perspective of parameterized algorithms. We believe that the parameter alphabet size that we introduce is likely to be useful in the context of optimization problems defined over permutation DAGs.

cs.DS↗

arXiv2020

Market Equilibrium in Multi-tier Supply Chain Networks

We consider a sequential decision model over multi-tier supply chain networks and show that in particular, for series parallel networks, there is a unique equilibrium. We provide a linear time algorithm to compute the equilibrium and study the impact and invariant of the network structure to the total trade flow and social welfare.

cs.GT↗

arXiv2020

On Variants of Network Flow Stability

We consider a general stable flow problem in a directed and capacitated network, where each vertex has a strict preference list over the incoming and outgoing edges. A flow is stable if no group of vertices forming a path can mutually benefit by rerouting the flow. Motivated by applications in supply chain networks, we generalize the traditional Kirchhoff's law, requiring the outflow is equal to the inflow at every nonterminal node, to a monotone piecewise linear relationship between the inflows and the outflows. We show the existence of a stable flow using Scarf's Lemma, and provide a polynomial time algorithm to find such a stable flow. We further show that finding a minimum cost generalized stable network is NP-hard, while the problem is polynomial time solvable for the traditional stable flow satisfying Kirchhoff's law.

cs.GT↗

arXiv2020

The Maximum Binary Tree Problem

We introduce and investigate the approximability of the maximum binary tree problem (MBT) in directed and undirected graphs. The goal in MBT is to find a maximum-sized binary tree in a given graph. MBT is a natural variant of the well-studied longest path problem, since both can be viewed as finding a maximum-sized tree of bounded degree in a given graph. The connection to longest path motivates the study of MBT in directed acyclic graphs (DAGs), since the longest path problem is solvable efficiently in DAGs. In contrast, we show that MBT in DAGs is in fact hard: it has no efficient $\exp(-O(\log n/ \log \log n))$-approximation algorithm under the exponential time hypothesis, where $n$ is the number of vertices in the input graph. In undirected graphs, we show that MBT has no efficient $\exp(-O(\log^{0.63}{n}))$-approximation under the exponential time hypothesis. Our inapproximability results rely on self-improving reductions and structural properties of binary trees. We also show constant-factor inapproximability assuming $\text{P}\neq \text{NP}$. In addition to inapproximability results, we present algorithmic results along two different flavors: (1) We design a randomized algorithm to verify if a given directed graph on $n$ vertices contains a binary tree of size $k$ in $2^k \text{poly}(n)$ time. (2) Motivated by the longest heapable subsequence problem, introduced by Byers, Heeringa, Mitzenmacher, and Zervas (ANALCO 2011), which is equivalent to MBT in permutation DAGs, we design efficient algorithms for MBT in bipartite permutation graphs.

cs.DM↗