arXiv subjects

Guangting Chen

Publications and source records attributed to Guangting Chen.

4 recordsLinked to original sources

arXiv2026

Near-Tight Approximation Algorithms for Bottleneck Multiple Knapsack Problems

In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the minimum profit received by any knapsack subject to the capacity constraint. When all knapsacks have identical capacity, we give a $(\frac{2}{3} - \varepsilon)$-approximation algorithm for any constant $\varepsilon > 0$. This result almost matches the $(\frac{2}{3} + \varepsilon)$ inapproximability bound for the bottleneck multiple subset sum problem (Caprara et al., 2000). When the knapsacks can have arbitrary capacities, we propose a $(\frac{1}{2} - \varepsilon)$-approximation algorithm for any constant $\varepsilon > 0$. We also prove a hardness bound of $(\frac{1}{2} + \varepsilon)$ for any constant $\varepsilon > 0$.

cs.DS↗

arXiv2025

Maximizing social welfare among EF1 allocations at the presence of two types of agents

We study the fair allocation of indivisible items to $n$ agents to maximize the utilitarian social welfare, where the fairness criterion is envy-free up to one item and there are only two different utility functions shared by the agents. We present a $2$-approximation algorithm when the two utility functions are normalized, improving the previous best ratio of $16 \sqrt{n}$ shown for general normalized utility functions; thus this constant ratio approximation algorithm confirms the APX-completeness in this special case previously shown APX-hard. When there are only three agents, i.e., $n = 3$, the previous best ratio is $3$ shown for general utility functions, and we present an improved and tight $\frac 53$-approximation algorithm when the two utility functions are normalized, and a best possible and tight $2$-approximation algorithm when the two utility functions are unnormalized.

cs.GT↗

arXiv2018

Approximation algorithms for two-machine flow-shop scheduling with a conflict graph

Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number of length-$0$ paths (that is, isolated vertices), turns out to be polynomial-time solvable. We further show that another variant, where the objective function is the total number of length-$0$ and length-$1$ paths, is also polynomial-time solvable. Both variants find applications in approximating the two-machine flow-shop scheduling problem in which job processing has constraints that are formulated as a conflict graph. For the unit jobs, we present a $4/3$-approximation algorithm for the scheduling problem with an arbitrary conflict graph, based on the exact algorithm for the variants of the path cover problem. For the arbitrary jobs while the conflict graph is the union of two disjoint cliques, that is, all the jobs can be partitioned into two groups such that the jobs in a group are pairwise conflicting, we present a simple $3/2$-approximation algorithm.

cs.DS↗

arXiv2017

On the NP-hardness of scheduling with time restrictions

In a recent paper, Braun, Chung and Graham [1] have addressed a single-processor scheduling problem with time restrictions. Given a fixed integer $B \geq 2$, there is a set of jobs to be processed by a single processor subject to the following B-constraint. For any real $x$, no unit time interval $[x, x+1)$ is allowed to intersect more than $B$ jobs. The problem has been shown to be NP-hard when $B$ is part of the input and left as an open question whether it remains NP-hard or not if $B$ is fixed [1, 5, 7]. This paper contributes to answering this question that we prove the problem is NP-hard even when $B=2$. A PTAS is also presented for any constant $B \geq 2$.

cs.DS↗