arXiv subjects

Markus Legner

Publications and source records attributed to Markus Legner.

12 recordsLinked to original sources

arXiv2025

Walrus: An Efficient Decentralized Storage Network

Decentralized storage faces a fundamental trade-off between replication overhead, recovery efficiency, and security guarantees. Current approaches either rely on full replication, incurring substantial storage costs, or employ erasure-coding schemes that struggle with efficient recovery, especially under high churn. We present Walrus, a decentralized blob storage system that addresses these limitations through multiple technical innovations. At the core of Walrus is Red Stuff, a two-dimensional erasure-coding protocol that achieves high security with only a 4.5x replication factor, while providing self-healing of lost data. This means that recovery is done without centralized coordination and requires bandwidth proportional to the amount of lost data. However, Red Stuff on its own is not sufficient for Walrus, as it is designed with a static set of participants in mind. To further support decentralization, we also introduce a multi-stage epoch-change protocol that efficiently handles storage node churn while maintaining uninterrupted availability during committee transitions. Our system incorporates authenticated data structures to defend against malicious clients and ensure data consistency throughout storage and retrieval. Walrus has been deployed in production since March 2025 and has secured 686 TB of data by July 2026. We conduct an experimental evaluation of the deployed system and demonstrate that Walrus achieves practical performance at scale and outperforms the Arweave decentralized storage system.

cs.DC↗

arXiv2023

Hummingbird: Fast, Flexible, and Fair Inter-Domain Bandwidth Reservations

To realize the long-standing vision of providing quality-of-service (QoS) guarantees on a public Internet, this paper introduces Hummingbird: a lightweight QoS-system that provides fine-grained inter-domain reservations for end hosts. Hummingbird enables flexible and composable reservations with end-to-end guarantees, and addresses an often overlooked, but crucial, aspect of bandwidth-reservation systems: incentivization of network providers. Hummingbird represents bandwidth reservations as tradable assets, allowing markets to emerge. These markets then ensure fair and efficient resource allocation and encourage deployment by remunerating providers. This incentivization is facilitated by decoupling reservations from network identities, which enables novel control-plane mechanisms and allows the design of a control plane based on smart contracts. Hummingbird also provides an efficient reservation data plane, which streamlines the processing on routers and thus simplifies the implementation, deployment, and traffic policing, while maintaining robust security properties. Our prototype implementation demonstrates the efficiency and scalability of Hummingbird's asset-based control plane, and our high-speed software implementation can fill a 160 Gbps link with Hummingbird packets on commodity hardware.

cs.NI↗

arXiv2022

Model-Based Insights on the Performance, Fairness, and Stability of BBR

Google's BBR is the most prominent result of the recently revived quest for efficient, fair, and flexible congestion-control algorithms (CCAs). While the performance of BBR has been investigated by numerous studies, previous work still leaves gaps in the understanding of BBR performance: Experiment-based studies generally only consider network settings that researchers can set up with manageable effort, and model-based studies neglect important issues like convergence. To complement previous BBR analyses, this paper presents a fluid model of BBRv1 and BBRv2, allowing both efficient simulation under a wide variety of network settings and analytical treatment such as stability analysis. By experimental validation, we show that our fluid model provides highly accurate predictions of BBR behavior. Through extensive simulations and theoretical analysis, we arrive at several insights into both BBR versions, including a previously unknown bufferbloat issue in BBRv2.

cs.NI↗

arXiv2021

An Axiomatic Perspective on the Performance Effects of End-Host Path Selection

In various contexts of networking research, end-host path selection has recently regained momentum as a design principle. While such path selection has the potential to increase performance and security of networks, there is a prominent concern that it could also lead to network instability (i.e., flow-volume oscillation) if paths are selected in a greedy, load-adaptive fashion. However, the extent and the impact vectors of instability caused by path selection are rarely concretized or quantified, which is essential to discuss the merits and drawbacks of end-host path selection. In this work, we investigate the effect of end-host path selection on various metrics of networks both qualitatively and quantitatively. To achieve general and fundamental insights, we leverage the recently introduced axiomatic perspective on congestion control and adapt it to accommodate joint algorithms for path selection and congestion control, i.e., multi-path congestion-control protocols. Using this approach, we identify equilibria of the multi-path congestion-control dynamics and analytically characterize these equilibria with respect to important metrics of interest in networks (the 'axioms') such as efficiency, fairness, and loss avoidance. Moreover, we analyze how these axiomatic ratings for a general network change compared to a scenario without path selection, thereby obtaining an interpretable and quantititative formalization of the performance impact of end-host path-selection. Finally, we show that there is a fundamental trade-off in multi-path congestion-control protocol design between efficiency, stability, and loss avoidance on one side and fairness and responsiveness on the other side.

cs.NI↗

arXiv2021

Enabling Novel Interconnection Agreements with Path-Aware Networking Architectures

Path-aware networks (PANs) are emerging as an intriguing new paradigm with the potential to significantly improve the dependability and efficiency of networks. However, the benefits of PANs can only be realized if the adoption of such architectures is economically viable. This paper shows that PANs enable novel interconnection agreements among autonomous systems, which allow to considerably improve both economic profits and path diversity compared to today's Internet. Specifically, by supporting packet forwarding along a path selected by the packet source, PANs do not require the Gao-Rexford conditions to ensure stability. Hence, autonomous systems can establish novel agreements, creating new paths which demonstrably improve latency and bandwidth metrics in many cases. This paper also expounds two methods to set up agreements which are Pareto-optimal, fair, and thus attractive to both parties. We further present a bargaining mechanism that allows two parties to efficiently automate agreement negotiations.

cs.NI↗

arXiv2021

GMA: A Pareto Optimal Distributed Resource-Allocation Algorithm

To address the rising demand for strong packet delivery guarantees in networking, we study a novel way to perform graph resource allocation. We first introduce allocation graphs, in which nodes can independently set local resource limits based on physical constraints or policy decisions. In this scenario we formalize the distributed path-allocation (PAdist) problem, which consists in allocating resources to paths considering only local on-path information -- importantly, not knowing which other paths could have an allocation -- while at the same time achieving the global property of never exceeding available resources. Our core contribution, the global myopic allocation (GMA) algorithm, is a solution to this problem. We prove that GMA can compute unconditional allocations for all paths on a graph, while never over-allocating resources. Further, we prove that GMA is Pareto optimal with respect to the allocation size, and it has linear complexity in the input size. Finally, we show with simulations that this theoretical result could be indeed applied to practical scenarios, as the resulting path allocations are large enough to fit the requirements of practically relevant applications.

cs.NI↗

arXiv2020

Incentivizing Stable Path Selection in Future Internet Architectures

By delegating path control to end-hosts, future Internet architectures offer flexibility for path selection. However, there is a concern that the distributed routing decisions by end-hosts, in particular load-adaptive routing, can lead to oscillations if path selection is performed without coordination or accurate load information. Prior research has addressed this problem by devising path-selection policies that lead to stability. However, little is known about the viability of these policies in the Internet context, where selfish end-hosts can deviate from a prescribed policy if such a deviation is beneficial fromtheir individual perspective. In order to achieve network stability in future Internet architectures, it is essential that end-hosts have an incentive to adopt a stability-oriented path-selection policy. In this work, we perform the first incentive analysis of the stability-inducing path-selection policies proposed in the literature. Building on a game-theoretic model of end-host path selection, we show that these policies are in fact incompatible with the self-interest of end-hosts, as these strategies make it worthwhile to pursue an oscillatory path-selection strategy. Therefore, stability in networks with selfish end-hosts must be enforced by incentive-compatible mechanisms. We present two such mechanisms and formally prove their incentive compatibility.

cs.NI↗

arXiv2017

Magnetic Weyl and Dirac Kondo semimetal phases in heterostructures

We study a layered three-dimensional heterostructure in which two types of Kondo insulators are stacked alternatingly. One of them is the topological Kondo insulator SmB 6 , the other one an isostructural Kondo insulator AB 6 , where A is a rare-earth element, e.g., Eu, Yb, or Ce. We find that if the latter orders ferromagnetically, the heterostructure generically becomes a magnetic Weyl Kondo semimetal, while antiferromagnetic order can yield a magnetic Dirac Kondo semimetal. We detail both scenarios with general symmetry considerations as well as concrete tight-binding calcu-lations and show that type-I as well as type-II magnetic Weyl/Dirac Kondo semimetal phases are possible in these heterostructures. Our results demonstrate that Kondo insulator heterostructures are a versatile platform for design of strongly correlated topological semimetals.

cond-mat.str-el↗

arXiv2016

Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions

The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows to extract a correlation length that diverges at topological phase transitions. The correlation length and the curvature function that defines the topological invariants are shown to have universal critical exponents, allowing the notion of universality classes to be introduced. Particularly in two dimensions, the universality class is determined by the orbital symmetry of the Dirac model. The scaling laws that constrain the critical exponents are revealed, and are predicted to be satisfied even in interacting systems, as demonstrated in an interacting topological Kondo Insulator.

cond-mat.mes-hall↗

arXiv2015

Surface-state spin textures and mirror Chern numbers in topological Kondo insulators

The recent discovery of topological Kondo insulators has triggered renewed interest in the well-known Kondo insulator samarium hexaboride, which is hypothesized to belong to this family. In this Letter, we study the spin texture of the topologically protected surface states in such a topological Kondo insulator. In particular, we derive close relationships between (i) the form of the hybridization matrix at certain high-symmetry points, (ii) the mirror Chern numbers of the system, and (iii) the observable spin texture of the topological surface states. In this way, a robust classification of topological Kondo insulators and their surface-state spin texture is achieved. We underpin our findings with numerical calculations of several simplified and realistic models for systems like samarium hexaboride.

cond-mat.str-el↗

arXiv2013

Topological invariants, surface states, and interaction-driven phase transitions in correlated Kondo insulators with cubic symmetry

We construct a lattice model for a cubic Kondo insulator consisting of one spin-degenerate $d$ and $f$ orbital at each lattice site. The odd-parity hybridization between the two orbitals permits us to obtain various trivial and topological insulating phases, which we classify in the presence of cubic symmetry. In particular, depending on the choice of our model parameters, we find a strong topological insulator phase with a band inversion at the $\mathrm{X}$ point, modeling the situation potentially realized in SmB$_6$, and a topological crystalline insulator phase with trivial $\mathbb{Z}_2$ indices but nonvanishing mirror Chern numbers. Using the Kotliar-Ruckenstein slave-boson scheme, we further demonstrate how increasing interactions among $f$ electrons can lead to topological phase transitions. Remarkably, for fixed band parameters, the $f$-orbital occupation number at the topological transitions is essentially independent of the interaction strength, thus yielding a robust criterion to discriminate between different phases.

cond-mat.str-el↗

arXiv2013

Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology

We study the entanglement spectrum of noninteracting band insulators, which can be computed from the two-point correlation function, when restricted to one part of the system. In particular, we analyze a type of partitioning of the system that maintains its full translational symmetry, by tracing over a subset of local degrees of freedom, such as sublattice sites or spin orientations. The corresponding single-particle entanglement spectrum is the band structure of an entanglement Hamiltonian in the Brillouin zone. We find that the hallmark of a nontrivial topological phase is a gapless entanglement spectrum with an "entanglement Fermi surface." Furthermore, we derive a relation between the entanglement spectrum and the quantum geometry of Bloch states contained in the Fubini-Study metric. The results are illustrated with lattice models of Chern insulators and Z_2 topological insulators.

cond-mat.str-el↗