arXiv subjects

Robert Streit

Publications and source records attributed to Robert Streit.

4 recordsLinked to original sources

arXiv2025

Constrained Cuts, Flows, and Lattice-Linearity

In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after precomputing a max-flow, so as to obtain parallel algorithms for min-cut problems with additional constraints encoded by lattice-linear predicates [3]. Some nice algorithmic applications follow. First, we use these methods to compute the irreducibles of the sublattice of min-cuts satisfying a regular predicate. By Birkhoff's theorem [4] this gives a succinct representation of such cuts, and so we also obtain a general algorithm for enumerating this sublattice. Finally, though we prove computing min-cuts satisfying additional constraints is NP-hard in general, we use poset slicing [5], [6] for exact algorithms with constraints not necessarily encoded by lattice-linear predicates) with better complexity than exhaustive search. We also introduce $k$-transition predicates and strong advancement for improved complexity analyses of lattice-linear predicate algorithms in parallel settings, which is of independent interest.

cs.DS↗

arXiv2024

Reducing Matroid Optimization to Basis Search

Much energy has been devoted to developing a matroid's computational properties, yet parallel algorithm design for matroid optimization seems less understood. Specifically, the current state of the art is a folklore reduction from optimization to the search based on methods originating in [KUW88]. However, while this reduction adds only constant overhead in terms of \emph{adaptive complexity}, it imposes a high cost in \emph{query complexity}. In response, we present a new reduction from optimization to search within the class of \emph{binary matroids} which, when $n$ and $r$ take the size of the ground set and matroid rank respectively, implies a novel optimization algorithm terminating in $\mathcal{O}(\sqrt{n}\cdot\log r)$ parallel rounds using only $\mathcal{O}(rn\cdot\log r)$ independence queries. This is a significant improvement in query complexity when the matroid is sparse, meaning $r \ll n$, while trading off only a logarithmic factor of the rank in the adaptive complexity. At a technical level, our method begins by observing that a basis is optimal if and only if it is the set of points of minimum weight in any cocircuit. Importantly, this certificate reveals that simultaneous tests for \emph{local optimality} in cocircuits is a general paradigm for parallel matroid optimization. By combining this idea with connections between bases and cocircuits we obtain our reduction, whose efficiency follows by analyzing the lattice of flats. A primary goal of our study is initiating a finer understanding of parallel matroid optimization. And so, since many of our techniques begin with observations about general matroids and their flats, we hope that our efforts aid the future design of parallel matroid algorithms and applications of lattice theory thereof.

cs.DS↗

arXiv2022

Achieving Almost All Blockchain Functionalities with Polylogarithmic Storage

In current blockchain systems, full nodes that perform all of the available functionalities need to store the entire blockchain. In addition to the blockchain, full nodes also store a blockchain-summary, called the \emph{state}, which is used to efficiently verify transactions. With the size of popular blockchains and their states growing rapidly, full nodes require massive storage resources in order to keep up with the scaling. This leads to a tug-of-war between scaling and decentralization since fewer entities can afford expensive resources. We present \emph{hybrid nodes} for proof-of-work (PoW) cryptocurrencies which can validate transactions, validate blocks, validate states, mine, select the main chain, bootstrap new hybrid nodes, and verify payment proofs. With the use of a protocol called \emph{trimming}, hybrid nodes only retain polylogarithmic number of blocks in the chain length in order to represent the proof-of-work of the blockchain. Hybrid nodes are also optimized for the storage of the state with the use of \emph{stateless blockchain} protocols. The lowered storage requirements should enable more entities to join as hybrid nodes and improve the decentralization of the system. We define novel theoretical security models for hybrid nodes and show that they are provably secure. We also show that the storage requirement of hybrid nodes is near-optimal with respect to our security definitions.

cs.CR↗

arXiv2021

Who Needs Consensus? A Distributed Monetary System Between Rational Agents via Hearsay

We propose a novel distributed monetary system called Hearsay that tolerates both Byzantine and rational behavior without the need for agents to reach consensus on executed transactions. Recent work [5, 10, 15] has shown that distributed monetary systems do not require consensus and can operate using a broadcast primitive with weaker guarantees, such as reliable broadcast. However, these protocols assume that some number of agents may be Byzantine and the remaining agents are perfectly correct. For the application of a monetary system in which the agents are real people with economic interests, the assumption that agents are perfectly correct may be too strong. We expand upon this line of thought by weakening the assumption of correctness and instead adopting a fault tolerance model which allows up to $t < \frac{N}{3}$ agents to be Byzantine and the remaining agents to be rational. A rational agent is one which will deviate from the protocol if it is in their own best interest. Under this fault tolerance model, Hearsay implements a monetary system in which all rational agents achieve agreement on executed transactions. Moreover, Hearsay requires only a single broadcast per transaction. In order to incentivize rational agents to behave correctly in Hearsay, agents are rewarded with transaction fees for participation in the protocol and punished for noticeable deviations from the protocol. Additionally, Hearsay uses a novel broadcast primitive called Rational Reliable Broadcast to ensure that agents can broadcast messages under Hearsay's fault tolerance model. Rational Reliable Broadcast achieves equivalent guarantees to Byzantine Reliable Broadcast [7] but can tolerate the presence of rational agents. To show this, we prove that following the Rational Reliable Broadcast protocol constitutes a Nash equilibrium between rational agents and may therefore be of independent interest.

cs.DC↗