The two player shortest path network interdiction problem

Interdicting Structured Combinatorial Optimization Problems with {0,1}-Objectives

Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been studied for a wide variety of classical combinatorial optimization problems, including maximum $s$-$t$ flows, shortest $s$-$t$ paths, maximum weight matchings, minimum spanning trees, maximum stable sets, and graph connectivity. Most interdiction problems are NP-hard, and furthermore, even designing efficient approximation algorithms that allow for estimati…

静态追捕场景下逃避者路径规划的动态规划方法

A Dynamic Programming Approach to Evader Pathfinding in Static Pursuit Scenarios

针对静态防御部署下的逃避者最优路径规划问题，提出DPERO算法，通过对数转换将生存目标转化为最短路径问题求解，在模拟网格中生存概率显著优于基线方法，可用于漏洞分析与战略规划。

The shortest game of Chinese Checkers and related problems

In 1979, David Fabian found a complete game of two-person Chinese Checkers in 30 moves (15 by each player) [Martin Gardner, Penrose Tiles to Trapdoor Ciphers, MAA, 1997]. This solution requires that the two players cooperate to generate a win as quickly as possible for one of them. We show, using computational search techniques, that no shorter game is possible. We also consider a solitaire version of Chinese Checkers where one player attempts to move her pieces across the board in as few moves as possible. In 1971, Octave Levenspiel found a solution in 27 moves [Ibid.]; we demonstrate that no…

Approximation Algorithms for Interdiction Problem with Packing Constraints

We study a bilevel optimization problem which is a zero-sum Stackelberg game. In this problem, there are two players, a leader and a follower, who pick items from a common set. Both the leader and the follower have their own (multi-dimensional) budgets, respectively. Each item is associated with a profit, which is the same to the leader and the follower, and will consume the leader's (follower's) budget if it is selected by the leader (follower). The leader and the follower will select items in a sequential way: First, the leader selects items within the leader's budget. Then the follower sele…

Solving Min-Max Problems with Applications to Games

We refine existing general network optimization techniques, give new characterizations for the class of problems to which they can be applied, and show that they can also be used to solve various two-player games in almost linear time. Among these is a new variant of the network interdiction problem, where the interdictor wants to destroy high-capacity paths from the source to the destination using a vertex-wise limited budget of arc removals. We also show that replacing the limit average in mean payoff games by the maximum weight results in a class of games amenable to these techniques.

Protection of flows under targeted attacks

Due to the importance of robustness in many real-world optimization problems, the field of robust optimization has gained a lot of attention over the past decade. We concentrate on maximum flow problems and introduce a novel robust optimization model which, compared to known models from the literature, features several advantageous properties: (i) We consider a general class of path-based flow problems which can be used to model a large variety of network routing problems (and other packing problems). (ii) We aim at solutions that are robust against targeted attacks by a potent adversary who m…

树上加权瓶颈汉明距离下的受限逆最优值问题

The Restricted Inverse Optimal Value Problem under Weighted Bottle-neck Hamming distance on trees

本文研究树上加权瓶颈汉明距离下的受限逆最优值问题，提出$O(n\log n)$时间算法，并进一步解决去除路径长度约束后的最小成本最短路径阻断问题，实验验证了算法的高效性。

一个煤格上的迪杰斯特拉算法

A Coalgebraic Dijkstra Algorithm

本文提出了一种煤格迪杰斯特拉算法，用于解决煤格最短路径问题，该问题是一个广泛优化问题的统一框架，涵盖了最短路径、 widest path 问题以及新的最短二叉树问题，并给出了算法的正确性条件和渐近复杂度。

Stackelberg Shortest Path Tree Game, Revisited

Let $G(V,E)$ be a directed graph with $n$ vertices and $m$ edges. The edges $E$ of $G$ are divided into two types: $E_F$ and $E_P$. Each edge of $E_F$ has a fixed price. The edges of $E_P$ are the priceable edges and their price is not fixed a priori. Let $r$ be a vertex of $G$. For an assignment of prices to the edges of $E_P$, the revenue is given by the following procedure: select a shortest path tree $T$ from $r$ with respect to the prices (a tree of cheapest paths); the revenue is the sum, over all priceable edges $e$, of the product of the price of $e$ and the number of vertices below $e…

通用时间可达性的价格

The Price of Universal Temporal Reachability

本文研究动态网络中的时间可达性问题，发现其无序价格与顶点数成正比，与静态网络的常数价格形成对比。

关于双层最短路径问题的复杂性

On the Complexity of the Bilevel Shortest Path Problem

本文研究了双层最短路径问题的复杂性，证明在不同情况下该问题的计算难度差异，并探讨了其在特定限制下的可解性。

Stackelberg Network Pricing Games

We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of $m$ priceable edges in a graph. The other edges have a fixed cost. Based on the leader's decision one or more followers optimize a polynomial-time solvable combinatorial minimization problem and choose a minimum cost solution satisfying their requirements based on the fixed costs and the leader's prices. The leader receives as revenue the total amount of prices paid by the followers for priceable edges in their solutions, and the problem is to find revenue maximizing…