Enoch Peserico, Michele Scquizzato
We present a simple proof that the competitive ratio of any randomized online matching algorithm for the line is at least $\sqrt{\log_2(n\!+\!1)}/12$ for all $n=2^i\!-\!1: i\in\mathbb{N}$.
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Colored Packets with Deadlines and Metric Space Transition Cost
我们考虑有色数据包的调度与转移成本，形成一个一般的度量空间。我们设计了一个$1 - O(\sqrt{MST(G) / L})$竞争算法。我们的主要结果是$1 - Ω(\sqrt{MST(G) / L})$的硬度结果，它分别匹配每个度量空间的算法的竞争比。特别地，我们改进了Azar在el处的硬度结果。2009年，为统一度量空间。我们还将我们的结果推广到服从三角不等式的加权有向图，并给出了一个$1 - O(\sqrt{TSP(G) / L})$竞争算法和一个近似匹配硬度结果。在证明我们的硬度结果时，我们使用了一些有趣的非标准嵌入。
Optimal competitiveness for Symmetric Rectilinear Steiner Arborescence and related problems
我们提出了两个相互关联的已知问题的最佳竞争算法，涉及施泰纳树形。一个是Berman和Coulston研究的对称直线Steiner树形图（SRSA）的连续问题。一个非常相关但离散的问题（过去单独研究）是在线网络上的在线多媒体内容分发（MCD）问题，最初由Papadimitriu，Ramanathan和Rangan提出。高效的内容交付被建模为他们定义的网络时间网格中的低成本Steiner树形图。我们在这里研究Charikar，Halperin和Motwani研究的版本（他们使用相同的问题定义，但删除了一些输入约束）。在上述论文中分别介绍的竞争比的界限是类似的两个问题：O（log N）的连续问题和O（log n）的网络问题，其中N是终端服务的数量，和n是网络的大小。下限分别为Omega（sqrt{log N}）和Omega（sqrt{log n}）。Berman和Coulston证明了上界和下界都是可以改进的。我们反驳这一猜想，并关闭这些二次差距的问题。我们首先提出了一个O（sqrt{log n}）的确定性竞争算法的MCD线上，匹配的下限。然后，我们将该算法转化为SRSA的竞争最优算法O（sqrt{log N}）。最后，我们将后者翻译回解决MCD问题，即使在请求数量很小的情况下（即O（min{sqrt{log n}，sqrt{log N}}）），这一次也是最优竞争。我们还提出了一个欧米茄…
We consider one of the simplest and best known buffer management architectures: the shared memory switch with multiple output queues and uniform packets. It was one of the first models studied by competitive analysis, with the Longest Queue Drop (LQD) buffer management policy shown to be at least $\sqrt{2}$- and at most $2$-competitive; a general lower bound of $4/3$ has been proven for all deterministic online algorithms. Closing the gap between $\sqrt{2}$ and $2$ has remained an open problem in competitive analysis for more than a decade, with only marginal success in reducing the upper boun…
Weighted $k$-Server Admits an Exponentially Competitive Algorithm
本文提出一个递归的随机在线算法，在均匀度量上实现加权$k$-服务器问题的$\exp(O(k^2))$竞争比，首次打破确定性算法的双重指数障碍，并推广到广义问题。
In this paper, we study two variants of the online metric matching problem. The first problem is the online metric matching problem where all the servers are placed at one of two positions in the metric space. We show that a simple greedy algorithm achieves the competitive ratio of 3 and give a matching lower bound. The second problem is the online facility assignment problem on a line, where servers have capacities, servers and requests are placed on 1-dimensional line, and the distances between any two consecutive servers are the same. We show lower bounds $1+ \sqrt{6}$ $(> 3.44948)$, $\frac…
Online Metric TSP: Beyond the $\sqrt{n}$ Barrier
该研究针对在线度量TSP，提出用m=(1+ε)n空间的确定性算法，竞争比达O(log³n/ε)，突破m=n时Θ(√n)的壁垒，同时证明m=n^(1+ε)时的下界，明确空间与竞争力的权衡关系。
A Tight $\widetilde Ω(\sqrt{m})$ Information-Theoretic Lower Bound for Randomized Online Set Cover
本文证明信息论随机化在线集合覆盖的紧致 $\Omega(\sqrt{m})$ 下界，表明即使计算无限，随机化也无法达到 $O(\log m)$ 竞争比，并推广到随机顺序模型和内存受限情形。
The bounded delay buffer management problem, which was proposed by Kesselman et~al.\ (STOC 2001 and SIAM Journal on Computing 33(3), 2004), is an online problem focusing on buffer management of a switch supporting Quality of Service (QoS). The problem definition is as follows: Packets arrive to a buffer over time and each packet is specified by the {\em release time}, {\em deadline} and {\em value}. An algorithm can transmit at most one packet from the buffer at each integer time and can gain its value as the {\em profit} if transmitting a packet by its deadline after its release time. The obj…
The \emph{Temp Secretary Problem} was recently introduced by Fiat et al. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved performance guarantees for cases already considered by Fiat et al.\ and give competitive ratios for new generalizations of the problem. In the classical setting, where candidates have identical contract durations $γ\ll 1$ and we are allowed to hire up to $B$ candidates simultaneously, our algorithm is $(\frac{1}{2} - O(\sqrtγ))$-competitive. For large $B$, the bound i…
Electrical Flows for Polylogarithmic Competitive Oblivious Routing
针对现有基于树的多对数竞争比无感知路由构造时间复杂度高、并行性差的问题，本文提出基于电流路由的方案，实现了更优的时间复杂度和并行深度。
Motivated by fairness requirements in communication networks, we introduce a natural variant of the online paging problem, called \textit{min-max} paging, where the objective is to minimize the maximum number of faults on any page. While the classical paging problem, whose objective is to minimize the total number of faults, admits $k$-competitive deterministic and $O(\log k)$-competitive randomized algorithms, we show that min-max paging does not admit a $c(k)$-competitive algorithm for any function $c$. Specifically, we prove that the randomized competitive ratio of min-max paging is $Ω(\log…
In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of revealed elements without using its numerical value. An algorithm is $α$ probability-competitive if every element from the optimum appears with probability $1/α$ in the output. We present a technique to design algorithms with strong probability-competitive ratios, improving the guarantees for almost every matroid class considered in the literature: e.g., we g…
Online Metric TSP
本文研究一般度量空间上的在线度量旅行商问题，提出竞争比为 O(√n) 的算法，消除了 d 维欧几里得空间中对维度的依赖，并证明无法同时达到一般度量 O(√n) 和一致度量 O(log n) 的最优竞争比。
A Simple $O(\log\log(\mathrm{rank}))$-Competitive Algorithm for the Matroid Secretary Problem
只有最近取得了进展，在获得$o(\log(\mathrm{rank}))$ -竞争算法的拟阵秘书问题。更准确地说，Chakraborty和Lachish（2012）提出了一个$O(\sqrt{\log(\mathrm{rank})})$竞争程序，Lachish（2014）后来提出了一个$O(\log\log(\mathrm{rank}))$竞争算法。这些算法及其分析都非常复杂，这也反映在它们的竞争比中的极高常数上。使用不同的工具，我们提出了一个相当简单的$O(\log\log(\mathrm{rank}))$竞争算法的拟阵秘书问题。我们的算法可以被解释为分布在一个简单的类型的拟阵秘书算法，这是很容易分析。由于我们的程序的简单性，我们也能够大大提高竞争比中的隐藏常数。
In most online problems with delay, clairvoyance (i.e. knowing the future delay of a request upon its arrival) is required for polylogarithmic competitiveness. In this paper, we show that this is not the case for set cover with delay (SCD) -- specifically, we present the first non-clairvoyant algorithm, which is $O(\log n \log m)$-competitive, where $n$ is the number of elements and $m$ is the number of sets. This matches the best known result for the classic online set cover (a special case of non-clairvoyant SCD). Moreover, clairvoyance does not allow for significant improvement - we present…
An $2\sqrt{k}$-approximation algorithm for minimum power $k$ edge disjoint $st$ -paths
针对最小功耗 k 条边不相交 st 路径问题，论文提出适用于一般边成本的 2√(2k) 近似算法，首次实现关于 k 的次线性近似保证。
Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top $K$ items from noisy pairwise comparisons. In our setting, we are non-actively given $r$ pairwise comparisons between each pair of $n$ items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity (SST) model. We analyze the competitive ratio of algorithms for the top-$K$ problem. In particular, we present a linear time algorithm for the top-$K$ problem which has a competitive ratio of $…
We consider the online Min-Sum Set Cover (MSSC), a natural and intriguing generalization of the classical list update problem. In Online MSSC, the algorithm maintains a permutation on $n$ elements based on subsets $S_1, S_2, \ldots$ arriving online. The algorithm serves each set $S_t$ upon arrival, using its current permutation $π_{t}$, incurring an access cost equal to the position of the first element of $S_t$ in $π_{t}$. Then, the algorithm may update its permutation to $π_{t+1}$, incurring a moving cost equal to the Kendall tau distance of $π_{t}$ to $π_{t+1}$. The objective is to minimize…
Learning-Augmented Online Algorithms for Nonclairvoyant Joint Replenishment Problem with Deadlines
本文提出一种利用预测的在线算法，解决有截止期限的联合补货问题，通过预测减少竞争比并提升性能。
We consider a natural extension to the metric uncapacitated Facility Location Problem (FLP) in which requests ask for different commodities out of a finite set $S$ of commodities. Ravi and Sinha (SODA'04) introduced the model as the Multi-Commodity Facility Location Problem (MFLP) and considered it an offline optimization problem. The model itself is similar to the FLP: i.e., requests are located at points of a finite metric space and the task of an algorithm is to construct facilities and assign requests to facilities while minimizing the construction cost and the sum over all assignment dist…
Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment
本文提出一个模块化非先知型框架，利用集合覆盖的通用算法将广义联合补货问题归约为TCP确认问题，匹配并改进现有竞争比，为多级聚合和加权对称次可加联合补货问题获得紧的$O(\sqrt{n})$竞争算法。
Optimal $k$-Secretary with Logarithmic Memory
本文提出一种使用对数内存的k-秘书算法，达到最优竞争比，通过将k-秘书问题转化为量化估计问题，改进了传统方法的内存需求。
Online Firefighting on Cactus Graphs
本文研究了仙人掌图上的在线灭火问题，提出了一种O(√n)竞争性的算法，并证明在特定条件下该问题的竞争比为3
The Greedy Binary Search Tree is Non-trivially Competitive
本研究证明$\textsf{Greedy}$二叉搜索树的竞争力为$2^{O(\root{}\root{}\text{log log }n)}$，采用缩放方法结合Wilber交错下界展开分析，为其$O(1)$竞争力的推测提供了非平凡的进展。
Improved Online Load Balancing in the Two-Norm
本文针对无关机器上的在线负载均衡问题，提出首个突破竞争比5的算法，达到4.9843，并通过新的原始-对偶框架统一证明了多个相关算法的最优性。
We analyze the problem of job scheduling with preempting on weighted jobs that can have either linear or exponential penalties. We review relevant literature on the problem and create and describe a few online algorithms that perform competitively with the optimal scheduler. We first describe a na{\" i}ve algorithm, which yields a high competitive ratio ($Ω(\frac{M}{s_{\min}})$) with the optimal, then provide an algorithm that yields a lower competitive ratio ($4\sqrt{\frac{M}{s_{\min}}} + n\log{\frac{Mn}{s_{\min}}}$). Finally, we make a minor modification to our algorithm to yield an algorith…
Huang et al.~(STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the ranking algorithm by Karp et al.~(STOC 1990) is strictly better than $0.5$-competitive and the problem is strictly harder than the online bipartite matching problem in that no algorithms can be $(1-1/e)$-competitive. This paper pins down two tight competitive ratios of classic algorithms for the fully online matching problem. For the fractional version of the pr…
Assigning channels via the meet-in-the-middle approach
我们研究了信道分配问题的复杂性。通过应用中间相遇方法，我们得到了一个在时间上运行的$\ell$有界信道分配算法（当边缘权重由$\ell$有界时）$O^*((2\sqrt{\ell+1})^n)$。这是第一个打破$(O(\ell))^n$障碍的算法。我们将该算法推广到计数型，代价是多项式因子略高。一个主要的开放问题是，对于独立于$\ell$的恒定$c$，信道分配是否允许$O(c^n)$时间算法。我们考虑一个类似的问题，广义T-着色，CSP问题，推广\CA。我们表明，广义T-着色不承认一个$2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$时间算法，其中$r$是实例的大小。
We study the problem of chasing convex bodies online: given a sequence of convex bodies $K_t\subseteq \mathbb{R}^d$ the algorithm must respond with points $x_t\in K_t$ in an online fashion (i.e., $x_t$ is chosen before $K_{t+1}$ is revealed). The objective is to minimize the sum of distances between successive points in this sequence. Bubeck et al. (STOC 2019) gave a $2^{O(d)}$-competitive algorithm for this problem. We give an algorithm that is $O(\min(d, \sqrt{d \log T}))$-competitive for any sequence of length $T$.
In this study, we investigated several online and semi-online scheduling problems on two hierarchical machines with a common due date to maximize the total early work. For the pure online case, we designed an optimal online algorithm with a competitive ratio of $\sqrt 2$. For the case when the total processing time is known, we proposed an optimal semi-online algorithm with a competitive ratio of $\frac{4}{3}$. Additionally, for the cases when the largest processing time is known, we gave optimal algorithms with a competitive ratio of $\frac{6}{5}$ if the largest job is a lower hierarchy one, …
Parallel $\mathcal O(\sqrt n)$ Overhead LSD Radix Sort
提出LSD基数排序变体Radsort，用 $\mathcal O(\sqrt n)$ 额外空间排序，具有稳定、实现简单且易并行化的特点，在处理超过约2MiB大小数组时优于传统非原位LSD基数排序。
Randomized algorithms for fully online multiprocessor scheduling with testing
针对带测试的完全在线多处理器调度问题，提出首个集成任意多确定性算法的随机化算法，在双机情形下期望竞争比优于已知确定性下界，并利用Yao原理证明了随机与确定性算法的竞争比下界。
We study the online bounded-delay packet scheduling problem (BDPS), where packets of unit size arrive at a router over time and need to be transmitted over a network link. Each packet has two attributes: a non-negative weight and a deadline for its transmission. The objective is to maximize the total weight of the transmitted packets. This problem has been well studied in the literature, yet its optimal competitive ratio remains unknown: the best upper bound is $1.828$, still quite far from the best lower bound of $ϕ\approx 1.618$. In the variant of BDPS with $s$-bounded instances, each packet…
Optimal competitiveness for the Rectilinear Steiner Arborescence problem
我们提出了两个相关的已知问题的最佳在线算法，包括斯坦纳树形，提高了下限和上限。其中之一是研究得很好的{ \em直角Steiner树形图}（$RSA$）的连续问题。我们将$RSA$的竞争比的上界和下界从$O(\log N)$和$Ω(\sqrt{\log N})$改进为$Θ(\frac{\log N}{\log \log N})$，其中$N$是Steiner点的个数.这将$RSA$和对称- $RSA$的竞争比分开，这两个问题的Berman和Coulston的界限是STOC 1997。第二个问题是Papadimitriou等人在几篇论文和Charikar等人的SODA 1998中提出的多媒体内容分发问题之一。它可以被看作是$RSA$的离散对应物（或网络对应物）。对于这第二个问题，我们提出了严格的界限，也在网络的大小，除了提出严格的界限，在斯坦纳点的数量（后者是类似的，我们推导出的$RSA$）。
The fractional knapsack problem is one of the classical problems in combinatorial optimization, which is well understood in the offline setting. However, the corresponding online setting has been handled only briefly in the theoretical computer science literature so far, although it appears in several applications. Even the previously best known guarantee for the competitive ratio was worse than the best known for the integral problem in the popular random order model. We show that there is an algorithm for the online fractional knapsack problem that admits a competitive ratio of 4.39. Our res…
In the chasing convex bodies problem, an online player receives a request sequence of $N$ convex sets $K_1,\dots, K_N$ contained in a normed space $\mathbb R^d$. The player starts at $x_0\in \mathbb R^d$, and after observing each $K_n$ picks a new point $x_n\in K_n$. At each step the player pays a movement cost of $||x_n-x_{n-1}||$. The player aims to maintain a constant competitive ratio against the minimum cost possible in hindsight, i.e. knowing all requests in advance. The existence of a finite competitive ratio for convex body chasing was first conjectured in 1991 by Friedman and Linial. …
Static Pricing for Single Sample Multi-unit Prophet Inequalities
本文研究了k单位单样本prophet不等式，证明当k≥3时，设置静态价格为第k大的样本可获得1/2的竞争比率，同时分析了大k情况下的最优静态定价方案。
The $k$-Fold Matroid Secretary Problem
本文提出了一种在 $k$-fold matroid 联合环境下，具有 $(1-O(\sqrt{\log(n)/k}))$ 竞争性的算法，扩展了 Kleinberg'05 的结果。
A Tight Competitive Ratio for Online Submodular Welfare Maximization
本文研究在线子模福利最大化问题，提出在随机到达顺序下竞争比为0.27493的算法，改进了之前1/4的保证。
A well-known theorem of Spencer shows that any set system with $n$ sets over $n$ elements admits a coloring of discrepancy $O(\sqrt{n})$. While the original proof was non-constructive, recent progress brought polynomial time algorithms by Bansal, Lovett and Meka, and Rothvoss. All those algorithms are randomized, even though Bansal's algorithm admitted a complicated derandomization. We propose an elegant deterministic polynomial time algorithm that is inspired by Lovett-Meka as well as the Multiplicative Weight Update method. The algorithm iteratively updates a fractional coloring while contro…
An All-Around Near-Optimal Solution for the Classic Bin Packing Problem
在本文中，我们提出了第一个算法与最佳的平均情况和接近最佳已知的最坏情况下的性能的经典在线装箱问题。长期以来，人们已经观察到，具有最佳平均情况性能的已知装箱算法在最坏情况意义上不是最佳的。特别是First Fit和Best Fit的最佳平均情况比为1，但最差情况竞争比为1.7。长度为$n$的均匀随机序列的第一拟合和最佳拟合的浪费空间预计分别为$Θ(n^{2/3})$和$Θ(\sqrt{n} \log ^{3/4} n)$。使用Harmonic算法可以将竞争比提高到1.691;该算法的进一步变化可以将竞争比降低到1.588。然而，Harmonic及其变体的平均性能较差;特别是，Harmonic的平均案例比约为1.27。本文首先介绍了一种简单的谐波匹配算法。该算法的平均性能与最佳拟合一样好，即，它的平均情况比为1，预期浪费空间为$Θ(\sqrt{n} \log ^{3/4} n)$。此外，该算法的竞争比与Harmonic一样好，即，它收敛到$ 1.691$，这是对最佳拟合和第一拟合的1.7的改进。我们还介绍了一种不同的算法，称为精炼谐波匹配，它实现了改进的竞争比的$1.636$，同时保持良好的平均情况下的性能谐波匹配和最佳拟合。最后，我们广泛的实验评估所研究的装箱算法表明，我们提出的算法具有可比的平均情况下的性能与最佳拟合和第一拟合，这也适用于序列，遵循分布以外的均匀分布。
Controlling Tail Risk in Online Ski-Rental
本文研究带尾部风险约束的在线滑雪租赁问题，发现限制竞争比超过特定值的概率会显著改变最优解结构，使购买概率变得非单调、不连续且可任意大。
Online Drone Coverage of Targets on a Line
研究无人机在线覆盖线状目标的问题，提出三种算法，针对不同视角角度α优化轨迹长度，证明竞争比上界，并给出α=π/4时的下界。
O(log log rank) Competitive-Ratio for the Matroid Secretary Problem
在\textit{Matroid Secretary Problem}（MSP）中，拟阵的基集的元素与其值被逐一在线显示。MSP的算法是\textit{Matroid-Unknown}，如果在其执行的每个阶段：（i）它只知道到目前为止已经揭示的元素及其值，以及（ii）它可以访问用于测试到目前为止已经揭示的元素的任何子集是否是独立集合的oracle。一个算法是\textit{Known-Cardinality}，如果除了（i）和（ii），它也知道初始基数的基集的拟阵。我们在这里提出了一个已知基数和\textit{Order-Oblivious}算法，以恒定的概率，选择一个独立的元素集，其值至少是最佳值除以$O(\log{\logρ})$，其中$ρ$是矩阵的秩;也就是说，该算法具有$O(\log{\logρ})$的\textit{competitive-ratio}。已知基数算法的最佳先前结果是Babaioff \textit{et al.}（2007）的$O(\logρ)$的竞争比，以及Chakraborty和Lachish（2012）的$O(\sqrt{\logρ})$的竞争比。在许多非平凡的情况下，我们提出的算法有一个竞争比是优于$O(\log{\logρ})$。它未能这样做的情况很容易描述。理解这些情况可能会导致问题的改进算法，或者相反，到非平凡的下限。
Scheduling with Obligatory Tests
针对含测试与处理两阶段的作业调度问题，采用竞争分析方法，证明1-SORT算法及阈值算法的竞争比上界，同时给出确定性算法的竞争比下界。
In the $d$-dimensional cow-path problem, a cow living in $\mathbb{R}^d$ must locate a $(d - 1)$-dimensional hyperplane $H$ whose location is unknown. The only way that the cow can find $H$ is to roam $\mathbb{R}^d$ until it intersects $\mathcal{H}$. If the cow travels a total distance $s$ to locate a hyperplane $H$ whose distance from the origin was $r \ge 1$, then the cow is said to achieve competitive ratio $s / r$. It is a classic result that, in $\mathbb{R}^2$, the optimal (deterministic) competitive ratio is $9$. In $\mathbb{R}^3$, the optimal competitive ratio is known to be at most $\ap…
Degree-bounded Online Bipartite Matching: OCS vs. Ranking
本研究针对$(d,d)$-有界图的在线二分匹配问题，对比分析Ranking与OCS两种经典算法，证明OCS在各固定$d\boldsymbol{\textit{geq}}2$及$d$趋于无穷时的竞争比均更优，并将结果拓展至$(k,d)$-有界图。
We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a single or multiple possibly unrelated machines that maximizes the number of jobs that complete before their deadline. Due to strong impossibility results for competitive analysis on a single machine, we require that jobs contain some slack $\varepsilon>0$, which means that the feasible time window for scheduling a job is at least $1+\varepsilon$ times its processing time on each eligibl…
Nearly Tight Bounds for the Online Sorting Problem
针对在线排序问题的指数级上下界差距，本文给出近紧界结果：在不同空间规模下实现O(log²n/ε)等竞争比，弥合差距并实现空间与竞争比的近最优权衡，还扩展至范围未知场景。
Improved Competitive Analysis of Online Scheduling Deadline-Sensitive Jobs
我们考虑下面的调度问题。只有一台机器，作业将在线完成。每个作业j都是抢占式的，当它到达时，它的其他特征立即显示给机器：截止日期要求，工作负载和价值。目标是最大化在截止日期前完成的工作的总价值。在[Lucier et al.，SPAA'13; Azar等人，EC'15]，获得2+f（s）的竞争比，其中大O符号f（s）= \mathcal{O}（\frac{1}{(\sqrt[3]{s}-1)^{2}}）和（2+f（s*b））/b，其中b=ω*（1-ω），ω在（0，1）中，并且s不小于1/b。在本文中，没有求助于在上述工作中使用的对偶拟合技术，我们提出了一个更简单，更直观的分析框架的两个算法，提高竞争比的第一个算法1，因此提高竞争比的第二个算法1/b。如[Lucier等人，SPAA'13; Azar等人EC'15]，在像用于云计算的在线批处理的场景中，松弛度s大是合理的，因此可以忽略上述竞争比率中的大O符号。在此假设下，我们的分析带来了非常显着的改善，这两个算法的竞争比：从2到1，从2/b到1/b分别。
Matroid Secretary for Regular and Decomposable Matroids
在拟阵秘书问题中，我们给出了一个元素流，并要求选择一组元素，使集合的总值最大化，前提是它是预先给定的拟阵的独立集。困难来自于这样一个假设，即决定是不可撤销的：如果我们选择接受一个元素时，它是由流，那么我们永远不能摆脱它，如果我们选择不接受它，那么我们不能后来添加它。Babaioff，Immorlica，和Kleinberg [SODA 2007]介绍了这个问题，给O（1）-竞争算法的某些类拟阵，证明了每个拟阵都有O（1）-竞争算法。然而，大多数已知允许O（1）-竞争算法的拟阵可以很容易地用图（例如图形和横向拟阵）表示。特别是，关于F-可表示拟阵（可以表示为域F上的向量空间的元素的拟阵类）知之甚少，这是基本拟阵类之一。此外，大多数已知的技术都依赖于图论，因为它们依赖于拟阵理论。我们超越了图，给出了一个O（1）-竞争算法的正规拟阵（类拟阵是表示在每一个领域），并使用技术，拟阵理论，而不是图论。我们使用的正则拟阵分解定理的西摩分解成拟阵的任何经常是图形，cographic，或同构的R_{10}，然后展示如何结合这些基本类的算法到一个算法的经常拟阵。这使我们能够超越正规拟阵推广到任何类的拟阵，承认这样的分解成类，我们已经有很好的算法。特别地，我们给出了一类最大流最小割拟阵的O（1）-竞争算法。
We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show that the largest processing time first (LPT) algorithm is 1.5-competitive. For the special case of two machines, Noga and Seiden (TCS 2001) introduce the SLEEPY algorithm that achieves a competitive ratio of $(5 - \sqrt{5})/2 \approx 1.382$, matching the lower bound by Chen and Vestjens (ORL 1997). Furthermore, Noga and Seiden note that in many applications one can kill a job and restart it later, and they leave an open problem whether algorithms with restart can obtain better competit…
On the Strong Matroid Secretary Conjecture and Beyond
本文通过有限线性规划验证并证明了强拟阵秘书猜想对所有线性拟阵成立，给出1/e竞争算法，并推广了单样本先知算法至任意拟阵。
Laminar Matroid Secretary: Greedy Strikes Back
针对层状拟阵秘书问题，本文提出简单贪心算法，将概率竞争比从既有禁忌集方法的 3√3≈5.196 改进至 4.75。
We consider evacuation of a group of $n \geq 2$ autonomous mobile agents (or robots) from an unknown exit on an infinite line. The agents are initially placed at the origin of the line and can move with any speed up to the maximum speed $1$ in any direction they wish and they all can communicate when they are co-located. However, the agents have different wireless communication abilities: while some are fully wireless and can send and receive messages at any distance, a subset of the agents are senders, they can only transmit messages wirelessly, and the rest are receivers, they can only recei…
Online Preemptive Matching Revisited
研究在线抢占式匹配问题，通过新方法证明该问题竞争比新上界0.5661，改进了之前的结果，且给出首个最优算法采用抢占时实例硬度的结果。
Competitive Kill-and-Restart and Preemptive Strategies for Non-Clairvoyant Scheduling
本文研究非clairvoyant调度中杀灭重启与抢占策略，给出确定性下界3及b-缩放策略的竞争比（确定性约6.197，随机化约3.032），并证明WSETF规则2-竞争，多机适配性能保证小于10。
Distributed Connectivity Decomposition
我们提出了时间有效的分布式算法分解图与大边或顶点连接到多个生成或支配树，分别。作为它们的主要应用，这些分解使我们能够实现信息流的大小接近的连接，通过并行化它沿着树。更具体地说，我们的分布式分解算法如下：（I）分解的每个无向图的顶点连通$k$到（分数）顶点不相交的加权支配树的总重量$Ω(\frac{k}{\log n})$，在$\widetilde{O}(D+\sqrt{n})$轮。(II)在$\widetilde{O}(D+\sqrt{nλ})$轮中，将每个具有边连通性$λ$的无向图分解为具有总权重$\lceil\frac{λ-1}{2}\rceil(1-\varepsilon)$的（分数）边不相交的加权生成树。我们还使用[Das Sarma等人，STOC'11]。此外，我们的顶点连通性分解扩展到集中式算法，并提高了[Censor-Hillel et al.，SODA'14]从$O(n^3)$到接近最佳的$\tilde{O}(m)$。作为推论，我们也得到了分布式不经意路由广播$O(1)$ -竞争的边缘拥塞和$O(\log n)$ -竞争的顶点拥塞。此外，顶点连通性分解导致接近时间最优的$O(\log n)$ -近似顶点连通性：集中式$\widetilde{O}(m)$和分布式$\tilde{O}(D+\sqrt{n})$。前者走向1974年的猜想Aho，Hopcroft和Ullma…
We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an $O(1)$-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an $O(\log n \log^2 r)$-competitive algorithm (where $r$ is the cardinality of the largest feasible subset). Inspired by the proof of our subadditive prophet inequality, we also obtain an $O(\log n \cdot \log^2 r)$-competitive algorithm for the Secreta…
On the Continuous CNN Problem
在（离散）CNN问题中，在线请求显示为$\mathbb{R}^2$中的点。每一个请求都必须在下一个请求出现之前完成。我们有一个服务器，它可以简单地通过将其$x$或$y$坐标与请求对齐来为请求提供服务。在线算法的目标是最小化服务器为服务所有请求而行进的总$L_1$距离。离散版本最著名的竞争比是879（由于Sitters和Stougie）。我们研究了连续版本，其中请求可以在$\mathbb{R}^2$中连续移动，服务器必须连续地服务请求。一个简单的对抗性论证表明，对于连续CNN问题，任何在线算法的竞争比的下限都是3。我们的主要贡献是一个在线算法的竞争比$3+2 \sqrt{3} \approx 6.464$。我们的分析很严密。连续版本推广了离散正交CNN问题，其中每个请求必须是$x$或与前一个请求对齐的$y$。因此，我们的结果改进了以前的最佳竞争比9（由于岩间和米泽）。
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