Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1601.07790

Topology Recognition and Leader Election in Colored Networks

Dariusz Dereniowski·Andrzej Pelc
View original source ↗Read source document ↗Export metadata ↓

Abstract

Topology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a single node adopting the label 1 (leader), with all other nodes adopting the label 0 and learning a path to the leader. We consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors, and ports at each node of degree $d$ are arbitrarily numbered $0,1,\dots, d-1$. Colored networks are generalizations both of labeled networks and anonymous networks. In colored networks, topology recognition and leader election are not always feasible. Hence we study two more general problems. The aim of the problem TOP (resp. LE), for a colored network and for input $I$ given to its nodes, is to solve topology recognition (resp. leader election) in this network, if this is possible under input $I$, and to have all nodes answer "unsolvable" otherwise. We show that nodes of a network can solve problems TOP and LE, if they are given, as input $I$, an upper bound $k$ on the number of nodes of a given color, called the size of this color. On the other hand we show that, if the nodes are given an input that does not bound the size of any color, then the answer to TOP and LE must be "unsolvable", even for the class of rings. Under the assumption that nodes are given an upper bound $k$ on the size of a given color, we study the time of solving problems TOP and LE in the $LOCAL$. We give an algorithm to solve each of these problems in arbitrary $n$-node networks of diameter $D$ in time $O(kD+D\log(n/D))$. We also show that this time is optimal, by exhibiting classes of networks in which every algorithm solving problems TOP or LE must use time $Ω(kD+D\log(n/D))$.

Explore related subjects

cs.DC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dariusz Dereniowski, Andrzej Pelc. 2016-01-28. Topology Recognition and Leader Election in Colored Networks. https://doi.org/10.1016/j.tcs.2016.01.037

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Concertina: Data-Centric Adaptive Pipeline Parallelism for Efficient Heterogeneous Long-Context LLM Training

Long context training is crucial for extending LLM context windows. Existing schemes, such as sequence parallelism, incur substantial communication overhead. Pipeline parallelism (PP) reduces this cost, but its effectiveness hinges on partitioning granularity. Batch-level PP employing sequence packing exhibits high memory consumption in long-context scenarios, whereas token-level PP splitting sequences into slices alleviates memory overhead but may introduce performance degradation. Moreover, the skewed sequence-length distribution in real-world datasets defeats any monolithic, static choice of PP granularity. In this paper, we propose \textit{Dynamic Pipeline Parallelism} (DPP), which transforms PP granularity from a static design choice into a workload-adaptive optimization space over packed, split, and hybrid chunks. DPP further introduces a new coupling between heterogeneous pipeline scheduling and gradient checkpointing. To solve this coupling, \name co-optimizes dynamic chunk scheduling with \textit{Stage-Aware Chunk-Level Adaptive Checkpointing}. Comprehensive experiments demonstrate that \name achieves up to 1.69\texttimes\ speedup over FlexSP and up to 1.40\texttimes\ over MEPipe. The source code is available at https://github.com/wsjdsg/InfiniPipe-code.

cs.DC↗
arXiv2026

A Low-Latency Semantic State Estimator using Latent Predictive Learning for Dynamic Network Monitoring and Orchestration

Closed-loop network monitoring and orchestration increasingly require semantic interpretations of live telemetry beyond raw counter collection. However, dynamic cloud-edge environments change both the active node set and the monitoring query at runtime, while control loops demand bounded millisecond-scale responses. We introduce a latent predictive state estimator (LPSE) for dynamic network monitoring and orchestration, built on latent predictive learning over streaming telemetry. The framework converts variable-cardinality node telemetry into topology-adaptive temporal representations, fuses them with monitoring questions, and returns bounded answers from a semantic codebook instead of autoregressive text generation. This design enables fixed-cost, single-pass inference while preserving semantic interpretability. By operating on permutation-invariant, slot-routed node representations keyed by stable identity, the model maintains a fixed input space and generalizes to node addition, removal, and reordering without retraining. Experimental results on a multi-node Kubernetes cluster show semantic prediction accuracy of 87.13% at approximately 72x lower mean inference latency compared to the lowest latency LLM tested.

cs.DC↗
arXiv2026

X-Stage: Modeling Post-Issue Backpressure in GPU Communication--Computation Fusion

Fine-grained, device-initiated communication allows fused GPU kernels to issue remote stores directly from their compute pipelines, a pattern increasingly used in expert parallelism (EP), tensor parallelism (TP), and Ulysses-style sequence parallelism (UP). Existing designs reason about where communication is issued and when remote data becomes ready, but lack a quantitative model of the sender-side interval after a remote store is accepted and before it becomes visible at the destination. This interval determines whether communication remains decoupled from computation or backpressures it. We identify X-Stage, a software-visible post-issue stage with finite decoupling. Downstream pressure can dissipate while the issuer resumes useful work, whereas sustained injection consumes X-Stage headroom and eventually stalls the compute pipeline. We characterize this behavior and build a calibrated model that predicts whether remote-store arrivals accumulate backpressure or recover during intervening computation. Guided by the model, we reshape bursty arrivals when they would exhaust X-Stage headroom and exploit natural compute windows when headroom can recover concurrently. Evaluation across representative EP, TP, and UP workloads shows up to 1.62x fused-kernel, 1.75x end-to-end, and 1.43x sender-visible speedup, respectively. Microbenchmarks further validate the model's predictions of backlog accumulation, recovery, and sender-side backpressure.

cs.DC↗