Colloquium on Structural Information & Communication Complexity最新文献

k-Center Clustering in Distributed Models 分布式模型中的 k 中心聚类

Colloquium on Structural Information & Communication Complexity Pub Date : 2024-07-25 DOI: 10.1007/978-3-031-60603-8_5

Leyla Biabani, A. Paz

引用次数: 0

On the Power of Threshold-Based Algorithms for Detecting Cycles in the CONGEST Model 基于阈值的算法在CONGEST模型中检测循环的能力

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-04-05 DOI: 10.48550/arXiv.2304.02360

P. Fraigniaud, Mael Luce, Ioan Todinca

{"title":"On the Power of Threshold-Based Algorithms for Detecting Cycles in the CONGEST Model","authors":"P. Fraigniaud, Mael Luce, Ioan Todinca","doi":"10.48550/arXiv.2304.02360","DOIUrl":"https://doi.org/10.48550/arXiv.2304.02360","url":null,"abstract":"It is known that, for every $kgeq 2$, $C_{2k}$-freeness can be decided by a generic Monte-Carlo algorithm running in $n^{1-1/Theta(k^2)}$ rounds in the CONGEST model. For $2leq kleq 5$, faster Monte-Carlo algorithms do exist, running in $O(n^{1-1/k})$ rounds, based on upper bounding the number of messages to be forwarded, and aborting search sub-routines for which this number exceeds certain thresholds. We investigate the possible extension of these threshold-based algorithms, for the detection of larger cycles. We first show that, for every $kgeq 6$, there exists an infinite family of graphs containing a $2k$-cycle for which any threshold-based algorithm fails to detect that cycle. Hence, in particular, neither $C_{12}$-freeness nor $C_{14}$-freeness can be decided by threshold-based algorithms. Nevertheless, we show that ${C_{12},C_{14}}$-freeness can still be decided by a threshold-based algorithm, running in $O(n^{1-1/7})= O(n^{0.857dots})$ rounds, which is faster than using the generic algorithm, which would run in $O(n^{1-1/22})simeq O(n^{0.954dots})$ rounds. Moreover, we exhibit an infinite collection of families of cycles such that threshold-based algorithms can decide $mathcal{F}$-freeness for every $mathcal{F}$ in this collection.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122815159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Minimum Cost Flow in the CONGEST Model 拥塞模型中的最小成本流

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-04-04 DOI: 10.48550/arXiv.2304.01600

Tijn de Vos

引用次数: 0

Lockless Blockchain Sharding with Multiversion Control 无锁区块链分片与多版本控制

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-03-30 DOI: 10.48550/arXiv.2303.17105

Ramesh Adhikari, C. Busch

{"title":"Lockless Blockchain Sharding with Multiversion Control","authors":"Ramesh Adhikari, C. Busch","doi":"10.48550/arXiv.2303.17105","DOIUrl":"https://doi.org/10.48550/arXiv.2303.17105","url":null,"abstract":"Sharding is used to address the performance and scalability issues of the blockchain protocols, which divides the overall transaction processing costs among multiple clusters of nodes. Shards require less storage capacity and communication and computation cost per node than the existing whole blockchain networks, and they operate in parallel to maximize performance. However, existing sharding solutions use locks for transaction isolation which lowers the system throughput and may introduce deadlocks. In this paper, we propose a lockless transaction method for ensuring transaction isolation without using locks, which improves the concurrency and throughput of the transactions. In our method, transactions are split into subtransactions to enable parallel processing in multiple shards. We use versions for the transaction accounts to implement consistency among the shards. We provide formal proof for liveness and correctness. We also evaluate experimentally our proposed protocol and compare the execution time and throughput with lock-based approaches. The experiments show that the transaction execution time is considerably shorter than the lock-based time and near to the ideal (no-lock) execution time.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130951002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Overcoming Probabilistic Faults in Disoriented Linear Search 无方向线性搜索中概率错误的克服

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-03-27 DOI: 10.48550/arXiv.2303.15608

Konstantinos Georgiou, Nikos Giachoudis, E. Kranakis

{"title":"Overcoming Probabilistic Faults in Disoriented Linear Search","authors":"Konstantinos Georgiou, Nikos Giachoudis, E. Kranakis","doi":"10.48550/arXiv.2303.15608","DOIUrl":"https://doi.org/10.48550/arXiv.2303.15608","url":null,"abstract":"We consider search by mobile agents for a hidden, idle target, placed on the infinite line. Feasible solutions are agent trajectories in which all agents reach the target sooner or later. A special feature of our problem is that the agents are $p$-faulty, meaning that every attempt to change direction is an independent Bernoulli trial with known probability $p$, where $p$ is the probability that a turn fails. We are looking for agent trajectories that minimize the worst-case expected termination time, relative to competitive analysis. First, we study linear search with one deterministic $p$-faulty agent, i.e., with no access to random oracles, $pin (0,1/2)$. For this problem, we provide trajectories that leverage the probabilistic faults into an algorithmic advantage. Our strongest result pertains to a search algorithm (deterministic, aside from the adversarial probabilistic faults) which, as $pto 0$, has optimal performance $4.59112+epsilon$, up to the additive term $epsilon$ that can be arbitrarily small. Additionally, it has performance less than $9$ for $pleq 0.390388$. When $pto 1/2$, our algorithm has performance $Theta(1/(1-2p))$, which we also show is optimal up to a constant factor. Second, we consider linear search with two $p$-faulty agents, $pin (0,1/2)$, for which we provide three algorithms of different advantages, all with a bounded competitive ratio even as $prightarrow 1/2$. Indeed, for this problem, we show how the agents can simulate the trajectory of any $0$-faulty agent (deterministic or randomized), independently of the underlying communication model. As a result, searching with two agents allows for a solution with a competitive ratio of $9+epsilon$, or a competitive ratio of $4.59112+epsilon$. Our final contribution is a novel algorithm for searching with two $p$-faulty agents that achieves a competitive ratio $3+4sqrt{p(1-p)}$.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126503497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exact Distributed Sampling 精确分布抽样

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-03-05 DOI: 10.48550/arXiv.2303.02714

S. Pemmaraju, Joshua Sobel

{"title":"Exact Distributed Sampling","authors":"S. Pemmaraju, Joshua Sobel","doi":"10.48550/arXiv.2303.02714","DOIUrl":"https://doi.org/10.48550/arXiv.2303.02714","url":null,"abstract":"Fast distributed algorithms that output a feasible solution for constraint satisfaction problems, such as maximal independent sets, have been heavily studied. There has been much less research on distributed sampling problems, where one wants to sample from a distribution over all feasible solutions (e.g., uniformly sampling a feasible solution). Recent work (Feng, Sun, Yin PODC 2017; Fischer and Ghaffari DISC 2018; Feng, Hayes, and Yin arXiv 2018) has shown that for some constraint satisfaction problems there are distributed Markov chains that mix in $O(log n)$ rounds in the classical LOCAL model of distributed computation. However, these methods return samples from a distribution close to the desired distribution, but with some small amount of error. In this paper, we focus on the problem of exact distributed sampling. Our main contribution is to show that these distributed Markov chains in tandem with techniques from the sequential setting, namely coupling from the past and bounding chains, can be used to design $O(log n)$-round LOCAL model exact sampling algorithms for a class of weighted local constraint satisfaction problems. This general result leads to $O(log n)$-round exact sampling algorithms that use small messages (i.e., run in the CONGEST model) and polynomial-time local computation for some important special cases, such as sampling weighted independent sets (aka the hardcore model) and weighted dominating sets.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134227392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Zero-Memory Graph Exploration with Unknown Inports 带有未知输入的零内存图探索

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-01-31 DOI: 10.48550/arXiv.2301.13860

Hans-Joachim Böckenhauer, F. Frei, Walter Unger, D. Wehner

{"title":"Zero-Memory Graph Exploration with Unknown Inports","authors":"Hans-Joachim Böckenhauer, F. Frei, Walter Unger, D. Wehner","doi":"10.48550/arXiv.2301.13860","DOIUrl":"https://doi.org/10.48550/arXiv.2301.13860","url":null,"abstract":"We study a very restrictive graph exploration problem. In our model, an agent without persistent memory is placed on a vertex of a graph and only sees the adjacent vertices. The goal is to visit every vertex of the graph, return to the start vertex, and terminate. The agent does not know through which edge it entered a vertex. The agent may color the current vertex and can see the colors of the neighboring vertices in an arbitrary order. The agent may not recolor a vertex. We investigate the number of colors necessary and sufficient to explore all graphs. We prove that n-1 colors are necessary and sufficient for exploration in general, 3 colors are necessary and sufficient if only trees are to be explored, and min(2k-3,n-1) colors are necessary and min(2k-1,n-1) colors are sufficient on graphs of size n and circumference $k$, where the circumference is the length of a longest cycle. This only holds if an algorithm has to explore all graphs and not merely certain graph classes. We give an example for a graph class where each graph can be explored with 4 colors, although the graphs have maximal circumference. Moreover, we prove that recoloring vertices is very powerful by designing an algorithm with recoloring that uses only 7 colors and explores all graphs.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133377143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Energy-Efficient Distributed Algorithms for Synchronous Networks 同步网络的高效分布式算法

Colloquium on Structural Information & Communication Complexity Pub Date : 2023-01-27 DOI: 10.48550/arXiv.2301.11988

P. Fraigniaud, Pedro Montealegre, I. Rapaport, Ioan Todinca

{"title":"Energy-Efficient Distributed Algorithms for Synchronous Networks","authors":"P. Fraigniaud, Pedro Montealegre, I. Rapaport, Ioan Todinca","doi":"10.48550/arXiv.2301.11988","DOIUrl":"https://doi.org/10.48550/arXiv.2301.11988","url":null,"abstract":"We study the design of energy-efficient algorithms for the LOCAL and CONGEST models. Specifically, as a measure of complexity, we consider the maximum, taken over all the edges, or over all the nodes, of the number of rounds at which an edge, or a node, is active in the algorithm. We first show that every Turing-computable problem has a CONGEST algorithm with constant node-activation complexity, and therefore constant edge-activation complexity as well. That is, every node (resp., edge) is active in sending (resp., transmitting) messages for only $O(1)$ rounds during the whole execution of the algorithm. In other words, every Turing-computable problem can be solved by an algorithm consuming the least possible energy. In the LOCAL model, the same holds obviously, but with the additional feature that the algorithm runs in $O(mbox{poly}(n))$ rounds in $n$-node networks. However, we show that insisting on algorithms running in $O(mbox{poly}(n))$ rounds in the CONGEST model comes with a severe cost in terms of energy. Namely, there are problems requiring $Omega(mbox{poly}(n))$ edge-activations (and thus $Omega(mbox{poly}(n))$ node-activations as well) in the CONGEST model whenever solved by algorithms bounded to run in $O(mbox{poly}(n))$ rounds. Finally, we demonstrate the existence of a sharp separation between the edge-activation complexity and the node-activation complexity in the CONGEST model, for algorithms bounded to run in $O(mbox{poly}(n))$ rounds. Specifically, under this constraint, there is a problem with $O(1)$ edge-activation complexity but $tilde{Omega}(n^{1/4})$ node-activation complexity.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133908506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Routing Schemes for Hybrid Communication Networks 混合通信网络的路由方案

Colloquium on Structural Information & Communication Complexity Pub Date : 2022-10-11 DOI: 10.1007/978-3-031-32733-9_14

Samantha R. Coy, A. Czumaj, C. Scheideler, P. Schneider, Julian Werthmann

引用次数: 1

Self-Adjusting Linear Networks with Ladder Demand Graph 阶梯需求图自调整线性网络

Colloquium on Structural Information & Communication Complexity Pub Date : 2022-07-08 DOI: 10.48550/arXiv.2207.03948

A. Paramonov, Iosif Salem, Stefan Schmid, V. Aksenov

{"title":"Self-Adjusting Linear Networks with Ladder Demand Graph","authors":"A. Paramonov, Iosif Salem, Stefan Schmid, V. Aksenov","doi":"10.48550/arXiv.2207.03948","DOIUrl":"https://doi.org/10.48550/arXiv.2207.03948","url":null,"abstract":"Self-adjusting networks (SANs) have the ability to adapt to communication demand by dynamically adjusting the workload (or demand) embedding, i.e., the mapping of communication requests into the network topology. SANs can thus reduce routing costs for frequently communicating node pairs by paying a cost for adjusting the embedding. This is particularly beneficial when the demand has structure, which the network can adapt to. Demand can be represented in the form of a demand graph, which is defined by the set of network nodes (vertices) and the set of pairwise communication requests (edges). Thus, adapting to the demand can be interpreted by embedding the demand graph to the network topology. This can be challenging both when the demand graph is known in advance (offline) and when it revealed edge-by-edge (online). The difficulty also depends on whether we aim at constructing a static topology or a dynamic (self-adjusting) one that improves the embedding as more parts of the demand graph are revealed. Yet very little is known about these self-adjusting embeddings. In this paper, the network topology is restricted to a line and the demand graph to a ladder graph, i.e., a $2^n$ grid, including all possible subgraphs of the ladder. We present an online self-adjusting network that matches the known lower bound asymptotically and is $12$-competitive in terms of request cost. As a warm up result, we present an asymptotically optimal algorithm for the cycle demand graph. We also present an oracle-based algorithm for an arbitrary demand graph that has a constant overhead.","PeriodicalId":116242,"journal":{"name":"Colloquium on Structural Information & Communication Complexity","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122152735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1