arXiv subjects

Mingyu Xiao

Publications and source records attributed to Mingyu Xiao.

At least 19 recordsLinked to original sources

arXiv2026

Two-Sided Screening in Quality-Differentiated Markets

Motivated by digital marketplaces such as Uber and Airbnb, we study how a two-sided platform designs a menu of qualities, consumer prices, and provider wages. Consumers and providers self-select according to their private values and costs, so the platform must design its menu to attract consumers while inducing enough supply to meet their demand. We study this coordination problem over a continuous quality space, requiring supply to cover demand at every quality threshold. We formulate menu design as an optimization over trading distributions, which specify how much trade occurs at or above each quality. Through convexification of the technological cost function, we characterize the profit- and welfare-optimal trading distributions. This characterization shows how production technology alone can reduce menu size without sacrificing optimal profit or welfare, regardless of the type distributions, and determines when optimal menus can be finite. We then show that profit maximization can be highly efficient: under monotone hazard rate conditions on both sides, a profit-optimal menu achieves at least $1/(e-1)$ of optimal social welfare. We next consider the practical setting in which the menu size is restricted to a prescribed number of offers. We establish how the restricted menu approximates the unrestricted optimum in profit. We develop an algorithm that computes a menu within this size limit in polynomial time. The computed menu simultaneously approximates the unrestricted optimal profit and social welfare with additive error.

cs.GT↗

arXiv2026

A Near-Linear Element-Kernel for $d$-Hitting Set

In $d$-Hitting Set, the input consists of a finite universe $U$, a family $\mathcal S$ of subsets of $U$ with size at most $d$, and an integer $k$. The task is to decide whether at most $k$ elements of $U$ can intersect every set in $\mathcal S$. Previously known kernels contain $O(k^{d-1})$ elements and $O(k^d)$ sets. Whether the number of elements can be reduced to $O(k^{d-1-\varepsilon})$ for some constant $\varepsilon>0$ is a longstanding open problem in kernelization. In this paper, we answer this question affirmatively by giving a near-linear randomized element-kernel and a subquadratic deterministic element-kernel through a re-encoding of the instance. For every fixed $d\geq3$, we give a one-sided randomized kernel with $O_d(k\log^3k)$ elements and a deterministic kernel with $O_d(k^{7/4}\log^{3/2}k)$ elements. Our kernels may still contain $k^{O(d)}$ sets and the parameter $k$ may grow polynomially.

cs.DS↗

arXiv2026

A Polynomial Kernel for Planar Directed Feedback Vertex Set

The Directed Feedback Vertex Set problem (DFVS) asks whether a digraph can be made acyclic by deleting at most $k$ vertices. Whether DFVS admits a polynomial kernel parameterized by $k$ is a major open problem in kernelization, even for planar digraphs. We resolve the planar case by giving a deterministic kernel with $O(k^{66}\log^2 k)$ vertices and arcs. Our algorithm proceeds in three stages. First, we apply structural reduction rules to the input digraph, bounding the number of directed faces and some special vertices. Second, we pass to the planar dual, where vertex deletion corresponds to adding groups of reverse arcs to make each weakly connected component strongly connected. The structural bounds in the first stage yield a small retained vertex set in the dual. We then compress the dual instance by identifying vertices with the same distance records from this retained vertex set. The main technical contribution is a directed-cut argument showing that this identification preserves feasibility. Finally, we transform the polynomial-size dual instance back into an instance of Planar Directed Feedback Vertex Set via a $3$-CNF encoding and a planar graph construction.

cs.DS↗

arXiv2026

Approximation and Inapproximability of Non-Preemptive Dial-a-Ride

The non-preemptive dial-a-ride problem (DaRP) asks for a minimum-cost route of a capacitated vehicle that serves a collection of pickup-and-delivery requests, without allowing objects to be transferred or temporarily unloaded. We study this problem and the closely related minimum-ratio Steiner $k$-Forest (S$k$F) in general symmetric metrics on $n$ locations. We develop a randomized polynomial-time algorithm with expected approximation ratio $\mathcal{O}(n^{1/4}\log^{11}n)$ for the minimum-ratio S$k$F. Our algorithm combines a deterministic approximation on hierarchically well-separated trees with randomized metric embeddings. Using this algorithm, we obtain expected $\mathcal{O}(n^{1/4}\log^{12}n)$-approximations for both the non-preemptive DaRP and the S$k$F. These guarantees improve on the previous $n^{0.3+\varepsilon}$-approximation ratios for the S$k$F and the non-preemptive DaRP, where $\varepsilon>0$ is any fixed constant. Complementing these algorithmic results, we establish the first superconstant inapproximability bounds for the non-preemptive DaRP. Under the Exponential Time Hypothesis (ETH), no deterministic polynomial-time algorithm achieves an $x^{1/(\log\log x)^c}$-approximation for some constant $c>0$, where $x$ denotes either the number of locations $n$ or the vehicle capacity $k$. Under the quantitative Gap-ETH, we rule out every deterministic polynomial-time $x^{o(1)}$-approximation. These bounds hold even on unit-edge stars with $n=(2+o(1))k$.

cs.DS↗

arXiv2026

How Hard Is It to Rig a Tournament When Few Players Can Beat or Be Beaten by the Favorite?

In knockout tournaments, players compete in successive rounds, with losers eliminated and winners advancing until a single champion remains. Given a tournament digraph $D$, which encodes the outcomes of all possible matches, and a designated player $v^* \in V(D)$, the \textsc{Tournament Fixing} problem (TFP) asks whether the tournament can be scheduled in a way that guarantees $v^*$ emerges as the winner. TFP is known to be NP-hard, but is fixed-parameter tractable (FPT) when parameterized by structural measures such as the feedback arc set (fas) or feedback vertex set (fvs) number of the tournament digraph. In this paper, we introduce and study two new structural parameters: the number of players who can defeat $v^*$ (i.e., the in-degree of $v^*$, denoted by $k$) and the number of players that $v^*$ can defeat (i.e., the out-degree of $v^*$, denoted by $\ell$). A natural question is that: can TFP be efficiently solved when $k$ or $\ell$ is small? We answer this question affirmatively by showing that TFP is FPT when parameterized by either the in-degree or out-degree of $v^*$. Our algorithm for the in-degree parameterization is particularly involved and technically intricate. Notably, the in-degree $k$ can remain small even when other structural parameters, such as fas or fvs, are large. Hence, our results offer a new perspective and significantly broaden the parameterized algorithmic understanding of the \textsc{Tournament Fixing} problem.

cs.GT↗

arXiv2026

The Role of Degrees and Acyclic Neighborhoods in the Complexity of Tournament Fixing

The \textsc{Tournament Fixing} problem asks whether a knockout tournament can be scheduled to make a favorite player win when all pairwise match outcomes are given. Such tournaments are used in sports and provide models for elections and organizational decision-making. Although the problem is NP-hard in general, it is polynomial-time solvable when some structural parameters become zero. Motivated by these cases, we study its parameterized complexity using those structural parameters centered on the favorite player. We prove fixed-parameter tractability when parameterized by either the number of players who beat the favorite player or the number that the favorite player beats. We next consider four subset parameters that measure the arc or vertex deletions needed to eliminate cycles through the player or either neighborhood. For each parameter, the problem remains NP-hard even when its value is one. When both neighborhoods are acyclic, we show that the problem remains NP-hard. We also give some sufficient conditions for the existence of a winning seeding. Our results complete the tractability classification of several individual parameters centered on the favorite player, extending the parameterized complexity landscape of this problem.

cs.GT↗

arXiv2026

Approximating Unsplittable Capacitated Vehicle Routing: Analysis via Factor-Revealing LPs

The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Given a depot and a set of customers with demands in a metric space, the objective is to find a set of tours, each starting and ending at the depot, operated by a capacitated vehicle located at the depot, such that all customers are served and the total travel cost is minimized. We consider the unsplittable variant, where the demand of each customer must be served entirely by a single tour. The previous best approximation ratio was about $α+1.694$, where $α$ is the approximation ratio for the traveling salesman problem. We propose improved approximation algorithms. First, we introduce a unified algorithmic framework that generalizes and integrates known linear programming (LP) rounding and matching-based approaches. We show that these techniques are complementary and can be combined to yield improved approximation ratios. Second, we develop a novel analytical framework based on customer demand discretization, which yields new structural bounds and, through factor-revealing LPs, achieves expected approximation ratios of about $α+1.647$ for the general-capacity case and $α+1.548$ for the fixed-capacity case. Finally, we derandomize our algorithms using a priori 2-tour sets and the method of conditional expectations while maintaining nearly the same approximation ratios.

cs.DS↗

arXiv2026

A Reduction-Driven Local Search for the Generalized Independent Set Problem

The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in fields such as forest harvest planning, competitive facility location, social network analysis, and even machine learning. However, solving the GIS problem in large-scale, real-world networks remains computationally challenging. In this paper, we explore data reduction techniques to address this challenge. We first propose 14 reduction rules that can reduce the input graph with rigorous optimality guarantees. We then present a reduction-driven local search (RLS) algorithm that integrates these reduction rules into the pre-processing, the initial solution generation, and the local search components in a computationally efficient way. The RLS is empirically evaluated on 278 graphs arising from different application scenarios. The results indicates that the RLS is highly competitive -- For most graphs, it achieves significantly superior solutions compared to other known solvers, and it effectively provides solutions for graphs exceeding 260 million edges, a task at which every other known method fails. Analysis also reveals that the data reduction plays a key role in achieving such a competitive performance.

cs.IR↗

arXiv2026

Tight Approximations for Fixed-Order Vehicle Routing with Stochastic Demands

We study the vehicle routing problem (VRP) with stochastic demands, where each client has an independent demand with a known distribution, and its realized demand is observed only on the first visit. We consider a priori and restocking policies that fix the client order before observing demands and serve each client's entire demand before first visiting the next. Gupta, Nagarajan, and Ravi (Oper. Res., 2012) developed randomized a priori $(α+1)$-approximation and $(α+2)$-approximation algorithms for splittable and unsplittable deliveries, respectively, where $α$ is the approximation ratio of a metric traveling salesman problem (TSP) algorithm. We improve these approximation ratios to $2$ and $3$ by using their replenishment rules with a TSP tour constructed via matroid parity. We also obtain deterministic a priori $(2+\varepsilon)$-approximation and $(3+\varepsilon)$-approximation algorithms by compressing the distributions of cumulative demands to select an initial stock in polynomial time. All guarantees are relative to the general adaptive optimum. We then establish matching lower bounds of $2$ and $3$ that hold even for the more general class of randomized restocking policies. Finally, we apply our matroid-parity construction to improve approximation ratios for several VRP variants with deterministic demands.

cs.DS↗

arXiv2026

Solving Restricted Versions of #SAT Faster than $2^m$: Algorithms and Lower Bounds

Under the Strong Exponential Time Hypothesis (SETH), for any constant $\varepsilon > 0$, the #SAT problem (counting the number of satisfying assignments of a CNF formula) cannot be solved in $\mathcal{O}^*((2-\varepsilon)^n)$ or $\mathcal{O}^*((2-\varepsilon)^m)$ time, where $n$ is the number of variables and $m$ is the number of clauses. On the other hand, simple exhaustive search and the standard inclusion-exclusion give $\mathcal{O}^*(2^n)$-time and $\mathcal{O}^*(2^m)$-time algorithms, respectively. A natural line of research is to beat these SETH-based barriers for restricted versions, such as #$k$-SAT (where each clause contains at most $k$ literals) or #$d$-occ-SAT (where each variable appears in at most $d$ clauses). It is known that the $2^n$-barrier can be broken when $k$ or $d$ is any constant; yet, whether the $2^m$-barrier can also be broken in these cases remains unknown. We present two simple algorithms that overcome the $2^m$-barrier. First, for #$k$-SAT, we give an $\mathcal{O}^*(2^{m(1-1/O(k))})$-time algorithm, thereby breaking the $2^m$-barrier for any constant $k$. Second, for #$2$-occ-SAT (which also includes the problem of counting the number of edge covers in a graph as a special case), we provide an algorithm with runtime $\mathcal{O}^*(2^{mω/3})$, where $ω< 2.3714$ is the matrix multiplication exponent. Furthermore, we demonstrate that both algorithms generalize to the weighted counting setting while preserving the same runtime bounds. On the hardness side, we present a reduction from #Max-$d$-SAT to #$d$-occ-SAT, showing that for any $d\ge 3$, #$d$-occ-SAT admits no $\mathcal{O}^*((2-\varepsilon)^m)$-time algorithm for any constant $\varepsilon>0$, even on positive formulas, under the hypothesis that #Max-3-SAT on $n$ variables admits no $\mathcal{O}^*((2-\varepsilon)^n)$-time algorithm for any such $\varepsilon$.

cs.DS↗

arXiv2026

A $(1+1/\sqrt{2})$-Approximation for the Multiple-Depot Traveling Salesman Problem

The metric traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization that asks for a minimum-cost tour covering all clients in a metric graph. The metric multiple-depot TSP (MD-TSP) is a natural extension, where the graph contains depots and clients, and the objective is to compute a minimum-cost set of tours covering all clients, with each tour starting and ending at the same depot. When the number of depots is part of the input, an adaptation of the Christofides--Serdyukov heuristic yields an approximation ratio of $2$. In this paper, we introduce a $(1+1/\sqrt{2})$-approximation algorithm. Like the Christofides--Serdyukov heuristic, our algorithm first computes a rooted spanning forest (RSF), then a matching to correct its odd degrees, and finally obtains a solution by shortcutting. However, instead of using a minimum-cost RSF, we construct an RSF by a primal-dual algorithm for a natural cut relaxation. The algorithm grows rootless components and the component containing all depots at different rates, adding an edge when its dual constraint becomes tight. Vertex labels record the times at which clients first become connected to a depot. The two-speed growth provides a joint bound on the forest cost and two label-dependent terms that also arise in bounding the parity-correction cost. Balancing the coefficients of these two terms by setting both to $\sqrt{2}-1$ yields the claimed approximation ratio.

cs.DS↗

arXiv2026

Improved Approximation Algorithms for the Multiple-Depot Split Delivery Vehicle Routing Problem

The multiple-depot split delivery vehicle routing problem is a challenging optimization problem with broad applications in logistics and transportation. The goal is to serve customers' demand using a limited fleet of capacitated vehicles stationed at multiple depots, allowing each customer's demand to be split and served by multiple vehicles, while minimizing the total travel cost. Parameterized by the number of depots, the previous best-known result was a slice-wise polynomial-time $6$-approximation algorithm (INFORMS J. Comput. 2023), and whether this ratio could be improved remained an open question. We resolve this question by proposing a fixed-parameter tractable (FPT) $(2α+1+\varepsilon)$-approximation algorithm for any constant $\varepsilon>0$, where $α<3/2$ denotes the best-known ratio for the traveling salesman problem (TSP). Our algorithm enumerates partitions of connected components formed by low-cost edges to construct a low-cost cycle cover, then extracts paths, and assigns them to vehicles through a minimum-cost flow method. The cycle-cover technique also yields an FPT $(α+\varepsilon)$-approximation for the multiple-depot TSP. We further propose a simple parameterized $5$-approximation algorithm based on the structural properties of vehicle capacities, which achieves polynomial running time for a specific setting that appears in existing benchmark instances. In addition, we develop a bi-factor approximation algorithm that balances minor vehicle capacity violations against reductions in travel cost or gains in computational efficiency. Finally, our computational experiments demonstrate that the proposed methods exhibit complementary strengths across various instance types and achieve competitive solution quality.

cs.DS↗

arXiv2026

Weighted Envy-Freeness Revisited: Indivisible Resource and House Allocations

Envy-Freeness is one of the most fundamental and important concepts in fair allocation. Some recent studies have focused on the concept of weighted envy-freeness. Under this concept, each agent is assigned a weight, and their valuations are divided by their weights when assessing fairness. This concept can promote more fairness in some scenarios. But on the other hand, experimental research has shown that this weighted envy-freeness significantly reduces the likelihood of fair allocations. When we must allocate the resources, we may propose fairness concepts with lower requirements that are potentially more feasible to implement. In this paper, we revisit weighted envy-freeness and propose a new concept called SumAvg-envy-freeness, which substantially increases the existence of fair allocations. This new concept can be seen as a complement of the normal weighted envy-fairness. Furthermore, we systematically study the computational complexity of finding fair allocations under the old and new weighted fairness concepts in two types of classic problems: Indivisible Resource Allocation and House Allocation. Our study provides a comprehensive characterization of various properties of weighted envy-freeness.

cs.GT↗

arXiv2026

Linear Kernels for $l$-Exact Component Order Connectivity

The \textsc{$l$-Exact Component Order Connectivity} problem asks whether, given an input graph $G$ and an integer $k$, there exists a vertex subset $S\subseteq V(G)$ of size at most $k$ such that every connected component in $G - S$ has exactly $l$ vertices. In this paper, we present an $O(kl)$-vertex kernel for this problem, computable in $|V(G)|^{O(l)}$ time. This is the first known linear kernel for each fixed $l\geq 3$. For $l=1$, this problem reduces to the classical \textsc{Vertex Cover}, and our result matches the best-known $2k$-vertex kernel. For $l=2$ (known as \textsc{Deletion to Induced Matching}), we can get a $(3k + 1)$-vertex kernel, improving the previously known result of $6k$ vertices. Our kernelization algorithm is built upon on an extended crown decomposition combined with linear programming and other techniques.

cs.DS↗

arXiv2026

Deterministic Single Exponential Time Algorithms for Co-Path Packing and Co-Path Set Parameterized by Treewidth

The \textsc{Co-Path Packing} (resp., \textsc{Co-Path Set}) problem asks whether a given graph can be edited to a collection of induced paths by deleting at most $k$ vertices (resp., $k$ edges). Both are fundamental problems with significant applications in bioinformatics and have been extensively studied within the framework of exact and parameterized algorithms. Currently, the state-of-the-art approach utilizes the randomized ``Cut \& Count'' technique, which solves \textsc{Co-Path Set} in $O^*(4^{\mathbf{tw}})$ time and \textsc{Co-Path Packing} in $O^*(5^{\mathbf{pw}})$ time, where $\mathbf{tw}$ is treewidth and $\mathbf{pw}$ is pathwidth. However, as there is no known method to derandomize the ``Cut \& Count'' technique, the existence of deterministic single exponential time algorithms for these problems parameterized by treewidth has remained an open question. In this paper, we resolve this gap by providing deterministic single exponential time algorithms for both problems when parameterized by treewidth.

cs.DS↗

arXiv2026

New Algorithms for Parity-SAT and Its Bounded-Occurrence Versions

Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT). Under the Strong Exponential Time Hypothesis (SETH), Parity-SAT admits no $O^*((2-\varepsilon)^n)$-time or $O^*((2-\varepsilon)^m)$-time algorithm for any constant $\varepsilon>0$, where $n$ and $m$ denote the numbers of variables and clauses, respectively. Thus, breaking the $2^n$ or $2^m$ barrier appears impossible in full generality. In this work, we revisit this barrier through structural restrictions and a refined exploitation of parity. We study Parity-$d$-occ-SAT, where each variable appears in at most $d$ clauses, and obtain three main results. First, we design a randomized $O^*(2^{m(1-1/O(d))})$-time algorithm, thereby breaking the $2^m$ barrier for every fixed $d$. Second, for the special case $d=2$, we develop a significantly sharper branching algorithm running in $O^*(1.1193^n)$ time or $O^*(1.3248^m)$ time. Third, leveraging the structural insights underlying the $d=2$ case, we obtain an $O^*(1.1052^L)$-time algorithm for general Parity-SAT, where $L$ denotes the formula length. All algorithms use only polynomial space. Notably, our running-time bounds are better than the best known bounds for the corresponding exact counting counterparts, highlighting a genuine algorithmic advantage of parity over counting. Conceptually, our results demonstrate that parity admits finer structural reductions and more efficient branching than exact model counting, and that bounded occurrence can be systematically leveraged to circumvent classical exponential barriers.

cs.DS↗

arXiv2026

Feedback Set Problems on Bounded-Degree (Planar) Graphs

The feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We obtain a complete complexity classification for these problems on bounded-degree digraphs, including the planar case. In particular, we show that both problems are $\NP$-complete on digraphs of maximum degree three, while on planar digraphs the feedback vertex set problem is polynomial-time solvable when each vertex has either indegree at most one or outdegree at most one, and $\NP$-complete otherwise. We also give tight degree bounds for the connected feedback vertex set problem on undirected graphs, both planar and non-planar. We close the paper with a historical account of results for feedback vertex set on undirected graphs of bounded degree.

cs.CC↗

arXiv2026

A Faster Deterministic Algorithm for Kidney Exchange via Representative Set

The Kidney Exchange Problem is a prominent challenge in healthcare and economics, arising in the context of organ transplantation. It has been extensively studied in artificial intelligence and optimization. In a kidney exchange, a set of donor-recipient pairs and altruistic donors are considered, with the goal of identifying a sequence of exchange -- comprising cycles or chains starting from altruistic donors -- such that each donor provides a kidney to the compatible recipient in the next donor-recipient pair. Due to constraints in medical resources, some limits are often imposed on the lengths of these cycles and chains. These exchanges create a network of transplants aimed at maximizing the total number, $t$, of successful transplants. Recently, this problem was deterministically solved in $O^*(14.34^t)$ time (IJCAI 2024). In this paper, we introduce the representative set technique for the Kidney Exchange Problem, showing that the problem can be deterministically solved in $O^*(6.855^t)$ time.

cs.DS↗