Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOnline Payment Network Design
83
0
0.0
(
0
)
Added by
Georgia Avarikioti
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Payment channels allow transactions between participants of the blockchain to be executed securely off-chain, and thus provide a promising solution for the scalability problem of popular blockchains. We study the online network design problem for payment channels, assuming a central coordinator. We focus on a single channel, where the coordinator desires to maximize the number of accepted transactions under given capital constraints. Despite the simplicity of the problem, we present a flurry of impossibility results, both for deterministic and randomized algorithms against adaptive as well as oblivious adversaries.
rate research
Read More
Payment channels are the most prominent solution to the blockchain scalability problem. We introduce the problem of network design with fees for payment channels from the perspective of a Payment Service Provider (PSP). Given a set of transactions, we examine the optimal graph structure and fee assignment to maximize the PSPs profit. A customer prefers to route transactions through the PSPs network if the cheapest path from sender to receiver is financially interesting, i.e., if the path costs less than the blockchain fee. When the graph structure is a tree, and the PSP facilitates all transactions, the problem can be formulated as a linear program. For a path graph, we present a polynomial time algorithm to assign optimal fees. We also show that the star network, where the center is an additional node acting as an intermediary, is a near-optimal solution to the network design problem.
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of linear programs for which such an algorithm is known. In this work we provide a distributed algorithm for solving a different class of convex programs which we call distance-bounded network design convex programs. These can be thought of as relaxations of network design problems in which the connectivity requirement includes a distance constraint (most notably, graph spanners). Our algorithm runs in $O( (D/epsilon) log n)$ rounds in the $mathcal{LOCAL}$ model and finds a $(1+epsilon)$-approximation to the optimal LP solution for any $0 < epsilon leq 1$, where $D$ is the largest distance constraint. While solving linear programs in a distributed setting is interesting in its own right, this class of convex programs is particularly important because solving them is often a crucial step when designing approximation algorithms. Hence we almost immediately obtain new and improved distributed approximation algorithms for a variety of network design problems, including Basic $3$- and $4$-Spanner, Directed $k$-Spanner, Lowest Degree $k$-Spanner, and Shallow-Light Steiner Network Design with a spanning demand graph. Our algorithms do not require any heavy computation and essentially match the best-known centralized approximation algorithms, while previous approaches which do not use heavy computation give approximations which are worse than the best-known centralized bounds.
Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they do not necessarily make consistent decisions. In this work we introduce time-local online algorithms. These are online algorithms where the output at a given time only depends on $T = O(1)$ latest inputs. The use of (deterministic) time-local algorithms in a distributed setting automatically leads to globally consistent decisions. Our key observation is that time-local online algorithms (in which the output at a given time only depends on local inputs in the temporal dimension) are closely connected to local distributed graph algorithms (in which the output of a given node only depends on local inputs in the spatial dimension). This makes it possible to interpret prior work on distributed graph algorithms from the perspective of online algorithms. We describe an algorithm synthesis method that one can use to design optimal time-local online algorithms for small values of $T$. We demonstrate the power of the technique in the context of a variant of the online file migration problem, and show that e.g. for two nodes and unit migration costs there exists a $3$-competitive time-local algorithm with horizon $T=4$, while no deterministic online algorithm (in the classic sense) can do better. We also derive upper and lower bounds for a more general version of the problem; we show that there is a $6$-competitive deterministic time-local algorithm and a $2.62$-competitive randomized time-local algorithm for any migration cost $alpha ge 1$.
We introduce a new model of computation: the online LOCAL model (OLOCAL). In this model, the adversary reveals the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each new node the algorithm can also inspect its radius-$T$ neighborhood before choosing the output; instead of looking ahead in time, we have the power of looking around in space. It is natural to compare OLOCAL with the LOCAL model of distributed computing, in which all nodes make decisions simultaneously in parallel based on their radius-$T$ neighborhoods.
Network decomposition is a central concept in the study of distributed graph algorithms. We present the first polylogarithmic-round deterministic distributed algorithm with small messages that constructs a strong-diameter network decomposition with polylogarithmic parameters. Concretely, a ($C$, $D$) strong-diameter network decomposition is a partitioning of the nodes of the graph into disjoint clusters, colored with $C$ colors, such that neighboring clusters have different colors and the subgraph induced by each cluster has a diameter at most $D$. In the weak-diameter variant, the requirement is relaxed by measuring the diameter of each cluster in the original graph, instead of the subgraph induced by the cluster. A recent breakthrough of Rozhov{n} and Ghaffari [STOC 2020] presented the first $text{poly}(log n)$-round deterministic algorithm for constructing a weak-diameter network decomposition where $C$ and $D$ are both in $text{poly}(log n)$. Their algorithm uses small $O(log n)$-bit messages. One can transform their algorithm to a strong-diameter network decomposition algorithm with similar parameters. However, that comes at the expense of requiring unbounded messages. The key remaining qualitative question in the study of network decompositions was whether one can achieve a similar result for strong-diameter network decompositions using small messages. We resolve this question by presenting a novel technique that can transform any black-box weak-diameter network decomposition algorithm to a strong-diameter one, using small messages and with only moderate loss in the parameters.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
