arXiv subjects

Jingyang Zhao

Publications and source records attributed to Jingyang Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Xiaomi Auto World Model: A Joint World Model Integrating Reconstruction and Generation for Autonomous Driving

This report presents a unified technical system addressing the two core capabilities of world models for autonomous driving: world representation and world generation. For world representation, we propose WorldRec, a feed-forward reconstruction architecture driven by sparse scene queries. WorldRec initializes structured queries in 3D space, leveraging them to aggregate cross-view, cross-temporal features, thereby naturally enforcing spatial consistency across frames and yielding compact yet high-fidelity 3D Gaussian scene representations. For world generation, we propose WorldGen, a two-stage training framework of bidirectional pretraining followed by causal fine-tuning through three progressive stages (Teacher Forcing, ODE distillation, and DMD), enabling high-quality online causal video generation in as few as 4 denoising steps. Building on both modules, we further introduce the JWM, which deeply integrates WorldRec and WorldGen to achieve synergistic gains in generation stability, cross-frame consistency, and visual fidelity, providing a solid foundation for closed-loop simulation, data synthesis, and end-to-end training in autonomous driving.

cs.CV↗

arXiv2026

Improved Approximations for Dial-a-Ride Problems

The multi-vehicle dial-a-ride problem (mDaRP) is a fundamental vehicle routing problem with pickups and deliveries, widely applicable in ride-sharing, economics, and transportation. Given a set of $n$ locations, $h$ vehicles of identical capacity $\lambda$ located at various depots, and $m$ ride requests each defined by a source and a destination, the goal is to plan non-preemptive routes that serve all requests while minimizing the total travel distance, ensuring that no vehicle carries more than $\lambda$ passengers at any time. The best-known approximation ratio for the mDaRP remains $\mathcal{O}(\sqrt{\lambda}\log m)$. We propose two simple algorithms: the first achieves the same approximation ratio of $\mathcal{O}(\sqrt{\lambda}\log m)$ with improved running time, and the second attains an approximation ratio of $\mathcal{O}(\sqrt{\frac{m}{\lambda}})$. A combination of them yields an approximation ratio of $\mathcal{O}(\sqrt[4]{n}\log^{\frac{1}{2}}n)$ under $m=\Theta(n)$. Moreover, for the case $m\gg n$, by extending our algorithms, we derive an $\mathcal{O}(\sqrt{n\log n})$-approximation algorithm, which also improves the current best-known approximation ratio of $\mathcal{O}(\sqrt{n}\log^2n)$ for the classic (single-vehicle) DaRP, obtained by Gupta et al. (ACM Trans. Algorithms, 2010).

cs.DS↗

arXiv2026

Improved Approximations for the Unsplittable Capacitated Vehicle Routing Problem

The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. In this problem, we are given a depot and a set of customers, each with a demand, embedded in a metric space. The objective is to find a set of tours, each starting and ending at the depot, operated by the capacititated vehicle at the depot to serve all customers, such that all customers are served, and the total travel cost is minimized. We consider the unplittable variant, where the demand of each customer must be served entirely by a single tour. Let $\alpha$ denote the current best-known approximation ratio for the metric traveling salesman problem. The previous best approximation ratio was $\alpha+1+\ln 2+\delta<3.1932$ for a small constant $\delta>0$ (Friggstad et al., Math. Oper. Res. 2025), which can be further improved by a small constant using the result of Blauth, Traub, and Vygen (Math. Program. 2023). In this paper, we propose two improved approximation algorithms. The first algorithm focuses on the case of fixed vehicle capacity and achieves an approximation ratio of $\alpha+1+\ln\bigl(2-\frac{1}{2}y_0\bigr)<3.0897$, where $y_0>0.39312$ is the unique root of $\ln\bigl(2-\frac{1}{2}y\bigr)=\frac{3}{2}y$. The second algorithm considers general vehicle capacity and achieves an approximation ratio of $\alpha+1+y_1+\ln\left(2-2y_1\right)+\delta<3.1759$ for a small constant $\delta>0$, where $y_1>0.17458$ is the unique root of $\frac{1}{2} y_1+ 6 (1-y_1)\bigl(1-e^{-\frac{1}{2} y_1}\bigr) =\ln\left(2-2y_1\right)$. Both approximations can be further improved by a small constant using the result of Blauth, Traub, and Vygen (Math. Program. 2023).

cs.DS↗

arXiv2026

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

The Multiple-Depot Split Delivery Vehicle Routing Problem (MD-SDVRP) is a challenging problem with broad applications in logistics. The goal is to serve customers' demand using a fleet of capacitated vehicles located in multiple depots, where each customer's demand can be served by more than one vehicle, while minimizing the total travel cost of all vehicles. We study approximation algorithms for this problem. Previously, the only known result was a $6$-approximation algorithm for a constant number of depots (INFORMS J. Comput. 2023), and whether this ratio could be improved was left as an open question. In this paper, we resolve it by proposing a $(6-2\cdot 10^{-36})$-approximation algorithm for this setting. Moreover, we develop constant-factor approximation algorithms that work beyond a constant number of depots, improved parameterized approximation algorithms related to the vehicle capacity and the number of depots, as well as bi-factor approximation algorithms.

cs.DS↗

arXiv2025

An Improved Approximation Algorithm for Maximum Weight 3-Path Packing

Given a complete graph with $n$ vertices and non-negative edge weights, where $n$ is divisible by 3, the maximum weight 3-path packing problem is to find a set of $n/3$ vertex-disjoint 3-paths such that the total weight of the 3-paths in the packing is maximized. This problem is closely related to the classic maximum weight matching problem. In this paper, we propose a $10/17$-approximation algorithm, improving the best-known $7/12$-approximation algorithm (ESA 2015). Our result is obtained by making a trade-off among three algorithms. The first is based on the maximum weight matching of size $n/2$, the second is based on the maximum weight matching of size $n/3$, and the last is based on an approximation algorithm for star packing. Our first algorithm is the same as the previous $7/12$-approximation algorithm, but we propose a new analysis method -- a charging method -- for this problem, which is not only essential to analyze our second algorithm but also may be extended to analyze algorithms for some related problems.

cs.DS↗

arXiv2025

An Improved Approximation Algorithm for the Capacitated Arc Routing Problem

The Capacitated Arc Routing Problem (CARP), introduced by Golden and Wong in 1981, is an important arc routing problem in Operations Research, which generalizes the famous Capacitated Vehicle Routing Problem (CVRP). When every customer has a unit demand, the best known approximation ratio for CARP, given by Jansen in 1993, remains $\frac{5}{2}-\frac{1.5}{k}$, where $k$ denotes the vehicle capacity. Based on recent progress in approximating CVRP, we improve this result by proposing a $(\frac{5}{2}-\Theta(\frac{1}{\sqrt{k}}))$-approximation algorithm, which to the best of our knowledge constitutes the first improvement over Jansen's bound.

cs.DS↗

arXiv2025

Approximation Algorithms for the Cumulative Vehicle Routing Problem with Stochastic Demands

In the Cumulative Vehicle Routing Problem (Cu-VRP), we need to find a feasible itinerary for a capacitated vehicle located at the depot to satisfy customers' demand, as in the well-known Vehicle Routing Problem (VRP), but the goal is to minimize the cumulative cost of the vehicle, which is based on the vehicle's load throughout the itinerary. If the demand of each customer is unknown until the vehicle visits it, the problem is called Cu-VRP with Stochastic Demands (Cu-VRPSD). Assume that the approximation ratio of metric TSP is $1.5$. In this paper, we propose a randomized $3.456$-approximation algorithm for Cu-VRPSD, improving the best-known approximation ratio of $6$ (Discret. Appl. Math. 2020). Since VRP with Stochastic Demands (VRPSD) is a special case of Cu-VRPSD, as a corollary, we also obtain a randomized $3.25$-approximation algorithm for VRPSD, improving the best-known approximation ratio of $3.5$ (Oper. Res. 2012). For Cu-VRP, we give a randomized $3.194$-approximation algorithm, improving the best-known approximation ratio of $4$ (Oper. Res. Lett. 2013). Moreover, if each customer is allowed to be satisfied by using multiple tours, we obtain further improvements for Cu-VRPSD and Cu-VRP.

cs.DS↗

arXiv2025

An Improved Algorithm for a Bipartite Traveling Tournament in Interleague Sports Scheduling

The bipartite traveling tournament problem (BTTP) addresses inter-league sports scheduling, which aims to design a feasible bipartite tournament between two $n$-team leagues under some constraints such that the total traveling distance of all participating teams is minimized. Since its introduction, several methods have been developed to design feasible schedules for NBA, NPB and so on. In terms of solution quality with a theoretical guarantee, previously only a $(2+\varepsilon)$-approximation is known for the case that $n\equiv 0 \pmod 3$. Whether there are similar results for the cases that $n\equiv 1 \pmod 3$ and $n\equiv 2 \pmod 3$ was asked in the literature. In this paper, we answer this question positively by proposing a $(3/2+\varepsilon)$-approximation algorithm for any $n$ and any constant $\varepsilon>0$, which also improves the previous approximation ratio for the case that $n\equiv 0 \pmod 3$.

cs.DS↗

arXiv2025

Enhanced Approximation Algorithms for the Capacitated Location Routing Problem

The Capacitated Location Routing Problem is an important planning and routing problem in logistics, which generalizes the capacitated vehicle routing problem and the uncapacitated facility location problem. In this problem, we are given a set of depots and a set of customers where each depot has an opening cost and each customer has a demand. The goal is to open some depots and route capacitated vehicles from the opened depots to satisfy all customers' demand, while minimizing the total cost. In this paper, we propose a $4.169$-approximation algorithm for this problem, improving the best-known $4.38$-approximation ratio. Moreover, if the demand of each customer is allowed to be delivered by multiple tours, we propose a more refined $4.091$-approximation algorithm. Experimental study on benchmark instances shows that the quality of our computed solutions is better than that of the previous algorithm and is also much closer to optimality than the provable approximation factor.

cs.DS↗

arXiv2025

Parameterized Approximation Algorithms for TSP on Non-Metric Graphs

The Traveling Salesman Problem (TSP) is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on metric graphs but becomes NP-hard to approximate within any computable function $f(n)$ on general graphs. This disparity highlights a significant gap between the results on metric graphs and general graphs. Recent research has introduced some parameters to measure the ``distance'' of general graphs from being metric and explored Fixed-Parameter Tractable (FPT) approximation algorithms parameterized by these parameters. Two commonly studied parameters are $p$, the number of vertices in triangles violating the triangle inequality, and $q$, the minimum number of vertices whose removal results in a metric graph. In this paper, we present improved FPT approximation algorithms with respect to these two parameters. For $p$, we propose an FPT algorithm with a 1.5-approximation ratio, improving upon the previous ratio of 2.5. For $q$, we significantly enhance the approximation ratio from 11 to 3, advancing the state of the art in both cases. In addition, when $p$ (or $q$) is a constant, we obtain a better approximation ratio.

cs.DS↗

arXiv2024

Approximation Algorithms for Packing Cycles and Paths in Complete Graphs

Given an edge-weighted (metric/general) complete graph with $n$ vertices, the maximum weight (metric/general) $k$-cycle/path packing problem is to find a set of $\frac{n}{k}$ vertex-disjoint $k$-cycles/paths such that the total weight is maximized. In this paper, we consider approximation algorithms. For metric $k$-cycle packing, we improve the previous approximation ratio from $3/5$ to $7/10$ for $k=5$, and from $7/8\cdot(1-1/k)^2$ for $k>5$ to $(7/8-0.125/k)(1-1/k)$ for constant odd $k>5$ and to $7/8\cdot (1-1/k+\frac{1}{k(k-1)})$ for even $k>5$. For metric $k$-path packing, we improve the approximation ratio from $7/8\cdot (1-1/k)$ to $\frac{27k^2-48k+16}{32k^2-36k-24}$ for even $10\geq k\geq 6$. For the case of $k=4$, we improve the approximation ratio from $3/4$ to $5/6$ for metric 4-cycle packing, from $2/3$ to $3/4$ for general 4-cycle packing, and from $3/4$ to $14/17$ for metric 4-path packing.

cs.DS↗

arXiv2024

Multidepot Capacitated Vehicle Routing with Improved Approximation Guarantees

The Multidepot Capacitated Vehicle Routing Problem (MCVRP) is a well-known variant of the classic Capacitated Vehicle Routing Problem (CVRP), where we need to route capacitated vehicles located in multiple depots to serve customers' demand such that each vehicle must return to the depot it starts, and the total traveling distance is minimized. There are three variants of MCVRP according to the property of the demand: unit-demand, splittable and unsplittable. We study approximation algorithms for $k$-MCVRP in metric graphs, where $k$ is the capacity of each vehicle. The best-known approximation ratios for the three versions are $4-Θ(1/k)$, $4-Θ(1/k)$, and $4$, respectively. We give a $(4-1/1500)$-approximation algorithm for unit-demand and splittable $k$-MCVRP, and a $(4-1/50000)$-approximation algorithm for unsplittable $k$-MCVRP. When $k$ is a fixed integer, we give a $(3+\ln2-\max\{Θ(1/\sqrt{k}),1/9000\})$-approximation algorithm for the splittable and unit-demand cases, and a $(3+\ln2-Θ(1/\sqrt{k}))$-approximation algorithm for the unsplittable case.

cs.DS↗

arXiv2024

The Traveling Tournament Problem: Improved Algorithms Based on Cycle Packing

The Traveling Tournament Problem (TTP) is a well-known benchmark problem in the field of tournament timetabling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, minimizing the total distance traveled by all $n$ teams ($n$ is even). TTP-$k$ is the problem with one more constraint that each team can have at most $k$-consecutive home games or away games. In this paper, we investigate schedules for TTP-$k$ and analyze the approximation ratio of the solutions. Most previous schedules were constructed based on a Hamiltonian cycle of the graph. We will propose a novel construction based on a $k$-cycle packing. Then, combining our $k$-cycle packing schedule with the Hamiltonian cycle schedule, we obtain improved approximation ratios for TTP-$k$ with deep analysis. The case where $k=3$, TTP-3, is one of the most investigated cases. We improve the approximation ratio of TTP-3 from $(1.667+\varepsilon)$ to $(1.598+\varepsilon)$, for any $\varepsilon>0$. For TTP-$4$, we improve the approximation ratio from $(1.750+\varepsilon)$ to $(1.700+\varepsilon)$. By a refined analysis of the Hamiltonian cycle construction, we also improve the approximation ratio of TTP-$k$ from $(\frac{5k-7}{2k}+\varepsilon)$ to $(\frac{5k^2-4k+3}{2k(k+1)}+\varepsilon)$ for any constant $k\geq 5$. Our methods can be extended to solve a variant called LDTTP-$k$ (TTP-$k$ where all teams are allocated on a straight line). We show that the $k$-cycle packing construction can achieve an approximation ratio of $(\frac{3k-3}{2k-1}+\varepsilon)$, which improves the approximation ratio of LDTTP-3 from $4/3$ to $(6/5+\varepsilon)$.

cs.DS↗

arXiv2024

An Improved Approximation Algorithm for Metric Triangle Packing

Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several simple methods can lead to a 2/3-approximation ratio. However, this barrier is not easy to break. Chen et al. proposed a randomized approximation algorithm with an expected ratio of $(0.66768-\varepsilon)$ for any constant $\varepsilon>0$. In this paper, we improve the approximation ratio to $(0.66835-\varepsilon)$. Furthermore, we can derandomize our algorithm.

cs.DS↗

arXiv2023

A $5$-approximation Algorithm for the Traveling Tournament Problem

The Traveling Tournament Problem (TTP-$k$) is a well-known benchmark problem in tournament timetabling, which asks us to design a double round-robin schedule such that the total traveling distance of all $n$ teams is minimized under the constraints that each pair of teams plays one game in each other's home venue, and each team plays at most $k$-consecutive home games or away games. Westphal and Noparlik (Ann. Oper. Res. 218(1):347-360, 2014) claimed a $5.875$-approximation algorithm for all $k\geq 4$ and $n\geq 6$. However, there were both flaws in the construction of the schedule and in the analysis. In this paper, we show that there is a $5$-approximation algorithm for all $k$ and $n$. Furthermore, if $k \geq n/2$, the approximation ratio can be improved to $4$.

cs.DS↗

arXiv2023

The APX-hardness of the Traveling Tournament Problem

The Traveling Tournament Problem (TTP-$k$) is a well-known benchmark problem in sports scheduling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, no pair of teams plays each other on two consecutive days, each team plays at most $k$ consecutive home games or away games, and the total traveling distance of all the $n$ teams is minimized. TTP-$k$ allows a polynomial-time approximation scheme when $k=2$ and becomes APX-hard when $k\geq n-1$. In this paper, we reduce the gap by showing that TTP-$k$ is APX-hard for any fixed $k\geq3$.

cs.DS↗

arXiv2023

PanGu-Coder2: Boosting Large Language Models for Code with Ranking Feedback

Large Language Models for Code (Code LLM) are flourishing. New and powerful models are released on a weekly basis, demonstrating remarkable performance on the code generation task. Various approaches have been proposed to boost the code generation performance of pre-trained Code LLMs, such as supervised fine-tuning, instruction tuning, reinforcement learning, etc. In this paper, we propose a novel RRTF (Rank Responses to align Test&Teacher Feedback) framework, which can effectively and efficiently boost pre-trained large language models for code generation. Under this framework, we present PanGu-Coder2, which achieves 62.20% pass@1 on the OpenAI HumanEval benchmark. Furthermore, through an extensive evaluation on CoderEval and LeetCode benchmarks, we show that PanGu-Coder2 consistently outperforms all previous Code LLMs.

cs.CL↗

arXiv2022

Practical Algorithms with Guaranteed Approximation Ratio for TTP with Maximum Tour Length Two

The Traveling Tournament Problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, minimizing the total distance traveled by all $n$ teams ($n$ is even). In this paper, we consider TTP-2, i.e., TTP under the constraint that at most two consecutive home games or away games are allowed for each team. We propose practical algorithms for TTP-2 with improved approximation ratios. Due to the different structural properties of the problem, all known algorithms for TTP-2 are different for $n/2$ being odd and even, and our algorithms are also different for these two cases. For even $n/2$, our approximation ratio is $1+3/n$, improving the previous result of $1+4/n$. For odd $n/2$, our approximation ratio is $1+5/n$, improving the previous result of $3/2+6/n$. In practice, our algorithms are easy to implement. Experiments on well-known benchmark sets show that our algorithms beat previously known solutions for all instances with an average improvement of $5.66\%$.

cs.DS↗