arXiv subjects

Tian Bai

Publications and source records attributed to Tian Bai.

23 records · Page 2Linked to original sources

arXiv2025

An Almost Quadratic Vertex Kernel for Subset Feedback Arc Set in Tournaments

In the Feedback Arc Set in Tournaments (Subset-FAST) problem, we are given a tournament $D$ and a positive integer $k$, and the objective is to determine whether there exists an arc set $S \subseteq A(D)$ of size at most $k$ whose removal makes the graph acyclic. This problem is well-known to be equivalent to a natural tournament ranking problem, whose task is to rank players in a tournament such that the number of pairs in which the lower-ranked player defeats the higher-ranked player is no more than $k$. Using the PTAS for Subset-FAST [STOC 2007], Bessy et al. [JCSS 2011] present a $(2 + \varepsilon)k$-vertex kernel for this problem, given any fixed $\varepsilon > 0$. A generalization of Subset-FAST, called Subset-FAST, further includes an additional terminal subset $T \subseteq V(D)$ in the input. The goal of Subset-FAST is to determine whether there is an arc set $S \subseteq A(D)$ of size at most $k$ whose removal ensures that no directed cycle passes through any terminal in $T$. Prior to our work, no polynomial kernel for Subset-FAST was known. In our work, we show that Subset-FAST admits an $\mathcal{O}((αk)^{2})$-vertex kernel, provided that Subset-FAST has an approximation algorithm with an approximation ratio $α$. Consequently, based on the known $\mathcal{O}(\log k \log \log k)$-approximation algorithm, we obtain an almost quadratic kernel for Subset-FAST.

cs.DS↗

arXiv2025

Breaking the Barrier $2^k$ for Subset Feedback Vertex Set in Chordal Graphs

The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set problem and Multiway Cut problem. SFVS remains NP-hard even in split and chordal graphs, and SFVS in Chordal Graphs (SFVS-C) can be considered as an implicit 3-Hitting Set problem. However, it is not easy to solve SFVS-C faster than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica 2019) proved that SFVS-C can be solved in $\mathcal{O}^{*}(2^{k})$ time, slightly improving the best result $\mathcal{O}^{*}(2.076^{k})$ for 3-Hitting Set. In this paper, we break the "$2^{k}$-barrier" for SFVS-C by giving an $\mathcal{O}^{*}(1.820^{k})$-time algorithm. Our algorithm uses reduction and branching rules based on the Dulmage-Mendelsohn decomposition and a divide-and-conquer method.

cs.DS↗

arXiv2024

Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model

The facility location game has been studied extensively in mechanism design. In the classical model, each agent's cost is solely determined by her distance to the nearest facility. In this paper, we introduce a novel model where each facility charges an entrance fee. Thus, the cost of each agent is determined by both the distance to the facility and the entrance fee of the facility. In our model, the entrance fee function is allowed to be an arbitrary function, causing agents' preferences may no longer be single-peaked anymore: This departure from the classical model introduces additional challenges. We systematically delve into the intricacies of the model, designing strategyproof mechanisms with favorable approximation ratios. Additionally, we complement these ratios with nearly-tight impossibility results. Specifically, for one-facility and two-facility games, we provide upper and lower bounds for the approximation ratios given by deterministic and randomized mechanisms with respect to utilitarian and egalitarian objectives.

cs.GT↗

arXiv2024

Facility Assignment with Fair Cost Sharing: Equilibrium and Mechanism Design

In the one-dimensional facility assignment problem, m facilities and n agents are positioned along the real line. Each agent will be assigned to a single facility to receive service. Each facility incurs a building cost, which is shared equally among the agents utilizing it. Additionally, each agent independently bears a connection cost to access a facility. Thus, an agent's cost is the sum of the connection cost and her portion of the building cost. The social cost is the total cost of all agents. Notably, the optimal assignment that minimizes the social cost can be found in polynomial time. In this paper, we study the problem from two game-theoretical settings regarding the strategy space of agents and the rule the assignment. In both settings, agents act strategically to minimize their individual costs. In our first setting, the strategy space of agents is the set of facilities, granting agents the freedom to select any facility. Consequently, the self-formed assignment can exhibit instability, as agents may deviate to other facilities. We focus on the computation of an equilibrium assignment, where no agent has an incentive to unilaterally change her choice. We show that we can compute a pure Nash equilibrium in polynomial time. In our second setting, agents report their positions to a mechanism for assignment to facilities. The strategy space of agents becomes the set of all positions. Our interest lies in strategyproof mechanisms. It is essential to note that the preference induced by the agents' cost function is more complex as it depends on how other agents are assigned. We establish a strong lower bound against all strategyproof and anonymous mechanisms: none can achieve a bounded social cost approximation ratio. Nonetheless, we identify a class of non-trivial strategyproof mechanisms for any n and m that is unanimous and anonymous.

cs.GT↗

arXiv2017

Faculty citation measures are highly correlated with peer assessment of computer science doctoral programs

We study relationship between peer assessment of quality of U.S. Computer Science (CS) doctoral programs and objective measures of research strength of those programs. In Fall 2016 we collected Google Scholar citation data for 4,352 tenure-track CS faculty from 173 U.S. universities. The citations are measured by the t10 index, which represents the number of citations received by the 10th highest cited paper of a faculty. To measure the research strength of a CS doctoral program we use 2 groups of citation measures. The first group of measures averages t10 of faculty in a program. Pearson correlation of those measures with the peer assessment of U.S. CS doctoral programs published by the U.S. News in 2014 is as high as 0.890. The second group of measures counts the number of well cited faculty in a program. Pearson correlation of those measures with the peer assessment is as high as 0.909. By combining those two groups of measures using linear regression, we create the Scholar score whose Pearson correlation with the peer assessment is 0.933 and which explains 87.2% of the variance in the peer assessment. Our evaluation shows that the highest 62 ranked CS doctoral programs by the U.S. News peer assessment are much higher correlated with the Scholar score than the next 57 ranked programs, indicating the deficiencies of peer assessment of less-known CS programs. Our results also indicate that university reputation might have a sizeable impact on peer assessment of CS doctoral programs. To promote transparency, the raw data and the codes used in this study are made available to research community at http://www.dabi.temple.edu/~vucetic/CSranking/.

cs.DL↗