arXiv subjects

Costas Busch

Publications and source records attributed to Costas Busch.

At least 19 recordsLinked to original sources

arXiv2025

A Poly-Log Approximation for Transaction Scheduling in Fog-Cloud Computing and Beyond

Transaction scheduling is crucial to efficiently allocate shared resources in a conflict-free manner in distributed systems. We investigate the efficient scheduling of transactions in a network of fog-cloud computing model, where transactions and their associated shared objects can move within the network. The schedule may require objects to move to transaction nodes, or the transactions to move to the object nodes. Moreover, the schedule may determine intermediate nodes where both objects and transactions meet. Our goal is to minimize the total combined cost of the schedule. We focus on networks of constant doubling dimension, which appear frequently in practice. We consider a batch problem where an arbitrary set of nodes has transactions that need to be scheduled. First, we consider a single shared object required by all the transactions and present a scheduling algorithm that gives an $O(\log n \cdot \log D)$ approximation of the optimal schedule, where $n$ is the number of nodes and $D$ is the diameter of the network. Later, we consider transactions accessing multiple shared objects (at most $k$ objects per transaction) and provide a scheduling algorithm that gives an $O(k \cdot \log n \cdot \log D)$ approximation. We also provide a fully distributed version of the scheduling algorithms where the nodes do not need global knowledge of transactions.

cs.DC↗

arXiv2025

Near-Optimal Stability for Distributed Transaction Processing in Blockchain Sharding

In blockchain sharding, $n$ processing nodes are divided into $s$ shards, and each shard processes transactions in parallel. A key challenge in such a system is to ensure system stability for any ``tractable'' pattern of generated transactions; this is modeled by an adversary generating transactions with a certain rate of at most $\rho$ and burstiness $b$. This model captures worst-case scenarios and even some attacks on transactions' processing, e.g., DoS. A stable system ensures bounded transaction queue sizes and bounded transaction latency. It is known that the absolute upper bound on the maximum injection rate for which any scheduler could guarantee bounded queues and latency of transactions is $\max\left\{ \frac{2}{k+1}, \frac{2}{ \left\lfloor\sqrt{2s}\right\rfloor}\right\}$, where $k$ is the maximum number of shards that each transaction accesses. Here, we first provide a single leader scheduler that guarantees stability under injection rate $\rho \leq \max\left\{ \frac{1}{16k}, \frac{1}{16\lceil \sqrt{s} \rceil}\right\}$. Moreover, we also give a distributed scheduler with multiple leaders that guarantees stability under injection rate $\rho \leq \frac{1}{16c_1 \log D \log s}\max\left\{ \frac{1}{k}, \frac{1}{\lceil \sqrt{s} \rceil} \right\}$, where $c_1$ is some positive constant and $D$ is the diameter of shard graph $G_s$. This bound is within a poly-log factor from the optimal injection rate, and significantly improves the best previous known result for the distributed setting by Adhikari et al., SPAA 2024.

cs.DC↗

arXiv2025

On the Efficiency of Dynamic Transaction Scheduling in Blockchain Sharding

Sharding is a technique to speed up transaction processing in blockchains, where the $n$ processing nodes in the blockchain are divided into $s$ disjoint groups (shards) that can process transactions in parallel. We study dynamic scheduling problems on a shard graph $G_s$ where transactions arrive online over time and are not known in advance. Each transaction may access at most $k$ shards, and we denote by $d$ the worst distance between a transaction and its accessing (destination) shards (the parameter $d$ is unknown to the shards). To handle different values of $d$, we assume a locality sensitive decomposition of $G_s$ into clusters of shards, where every cluster has a leader shard that schedules transactions for the cluster. We first examine the simpler case of the stateless model, where leaders are not aware of the current state of the transaction accounts, and we prove a $O(d \log^2 s \cdot \min\{k, \sqrt{s}\})$ competitive ratio for latency. We then consider the stateful model, where leader shards gather the current state of accounts, and we prove a $O(\log s\cdot \min\{k, \sqrt{s}\}+\log^2 s)$ competitive ratio for latency. Each leader calculates the schedule in polynomial time for each transaction that it processes. We show that for any $\epsilon > 0$, approximating the optimal schedule within a $(\min\{k, \sqrt{s}\})^{1 -\epsilon}$ factor is NP-hard. Hence, our bound for the stateful model is within a poly-log factor from the best possibly achievable. To the best of our knowledge, this is the first work to establish provably efficient dynamic scheduling algorithms for blockchain sharding systems.

cs.DC↗

arXiv2024

Fast Transaction Scheduling in Blockchain Sharding

Sharding is a promising technique for addressing the scalability issues of blockchain, and this technique is especially important for IoT, edge, or mobile computing. It divides the $n$ participating nodes into $s$ disjoint groups called shards, where each shard processes transactions in parallel. We examine batch scheduling problems on the shard graph $G_s$, where we find efficient schedules for a set of transactions. First, we present a centralized scheduler where one of the shards is considered as a leader, who receives the transaction information from all of the other shards and determines the schedule to process the transactions. For general graphs, where a transaction and its accessing objects are arbitrarily far from each other with a maximum distance $d$, the centralized scheduler provides $O(kd)$ approximation to the optimal schedule, where $k$ is the maximum number of shards each transaction accesses. Next, we provide a centralized scheduler with a bucketing approach that offers improved bounds for the case where $G_s$ is a line graph, or the $k$ objects are randomly selected. Finally, we provide a distributed scheduler where shards do not require global transaction information. We achieve this by using a hierarchical clustering of the shards and using the centralized scheduler in each cluster. We show that the distributed scheduler has a competitive ratio of $O(A_{CS} \cdot \log d \cdot \log s)$, where $A_{CS}$ is the approximation ratio of the centralized scheduler. To our knowledge, we are the first to give provably fast transaction scheduling algorithms for blockchain sharding systems. We also present simulation results for our schedulers and compare their performance with a lock-based approach. The results show that our schedulers are generally better with up to 3x lower latency and 2x higher throughput.

cs.DC↗

arXiv2024

Stable Blockchain Sharding under Adversarial Transaction Generation

Sharding is used to improve the scalability and performance of blockchain systems. We investigate the stability of blockchain sharding, where transactions are continuously generated by an adversarial model. The system consists of $n$ processing nodes that are divided into $s$ shards. Following the paradigm of classical adversarial queuing theory, transactions are continuously received at injection rate $\rho \leq 1$ and burstiness $b > 0$. We give an absolute upper bound $\max\{ \frac{2}{k+1}, \frac{2}{ \left\lfloor\sqrt{2s}\right\rfloor}\}$ on the maximum injection rate for which any scheduler could guarantee bounded queues and latency of transactions, where $k$ is the number of shards that each transaction accesses. We next give a basic distributed scheduling algorithm for uniform systems where shards are equally close to each other. To guarantee stability, the injection rate is limited to $\rho \leq \max\{ \frac{1}{18k}, \frac{1}{\lceil 18 \sqrt{s} \rceil} \}$. We then provide a fully distributed scheduling algorithm for non-uniform systems where shards are arbitrarily far from each other. By using a hierarchical clustering of the shards, stability is guaranteed with injection rate $\rho \leq \frac{1}{c_1d \log^2 s} \cdot \max\{ \frac{1}{k}, \frac{1}{\sqrt{s}} \}$, where $d$ is the worst distance of any transaction to the shards it will access, and $c_1$ is some positive constant. We also conduct simulations to evaluate the algorithms and measure the average queue sizes and latency throughout the system. To our knowledge, this is the first adversarial stability analysis of sharded blockchain systems.

cs.DC↗

arXiv2023

One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree

A spanning tree $T$ of graph $G$ is a $\rho$-approximate universal Steiner tree (UST) for root vertex $r$ if, for any subset of vertices $S$ containing $r$, the cost of the minimal subgraph of $T$ connecting $S$ is within a $\rho$ factor of the minimum cost tree connecting $S$ in $G$. Busch et al. (FOCS 2012) showed that every graph admits $2^{O(\sqrt{\log n})}$-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both $O(\log ^ 7 n)$-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to $O(\log n)$-approximate USTs and $O(1)$ strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

cs.DS↗

arXiv2023

Lockless Blockchain Sharding with Multiversion Control

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.

cs.DC↗

arXiv2022

Stable Scheduling in Transactional Memory

We study computer systems with transactions executed on a set of shared objects. Transactions arrive continually subjects to constrains that are framed as an adversarial model and impose limits on the average rate of transaction generation and the number of objects that transactions use. We show that no deterministic distributed scheduler in the queue-free model of transaction autonomy can provide stability for any positive rate of transaction generation. Let a system consist of $m$ shared objects and an adversary be constrained such that each transaction may access at most $k$ shared objects. We prove that no scheduler can be stable if a generation rate is greater than $\max\bigl\{\frac{2}{k+1},\frac{2}{\lfloor \sqrt{2m} \rfloor}\bigr\}$. We develop a centralized scheduler that is stable if a transaction generation rate is at most $\max\bigl\{\frac{1}{4k}, \frac{1}{4\lceil\sqrt{m}\rceil} \bigr\}$. We design a distributed scheduler in the queue-based model of transaction autonomy, in which a transaction is assigned to an individual processor, that guarantees stability if the rate of transaction generation is less than $\max\bigl\{ \frac{1}{6k},\frac{1}{6\lceil\sqrt{m}\rceil}\bigr\}$. For each of the schedulers we give upper bounds on the queue size and transaction latency in the range of rates of transaction generation for which the scheduler is stable.

cs.DC↗

arXiv2022

Fault-Tolerant Distributed Directories

A distributed directory is an overlay data structure on a graph $G$ that helps to access a shared token $t$. The directory supports three operations: publish, to announce the token, lookup, to read the contents of the token, and move, to get exclusive update access to the token. The directory is built upon a hierarchical partition of the graph using either weak or strong clusters. The main mechanism is the maintenance of a directory path that starts at the root node in the hierarchy and points to the current owner of the token. In the literature, there are known directory algorithms based on hierarchical graph structures, but none of them have considered failures. Given a hierarchical partition, we consider the impact of $f$ edge failures on the functionality and performance of the distributed directory. The edge failures may result in the splitting of clusters into up to $f+1$ connected components and an increase in the number of levels in the hierarchy. To recover the hierarchical partition after failures, we maintain spanning trees in the clusters and their connected components. If $G$ remains connected, we show that each level of the directory path is dilated by only a factor $f$. We also show that the performance of the publish and lookup operations is affected in the worst case by a factor $f$ with respect to the message complexity. The message complexity of the move operation increases by an $f$ factor and the number of additional layers in the hierarchy.

cs.DC↗

arXiv2021

Byzantine-Resilient Population Protocols

Population protocols model information spreading and computation in network systems where pairwise node exchanges are determined by an external random scheduler and nodes have small memory. Most of the population protocols in the literature assume that the participating $n$ nodes are honest. Such an assumption may not be, however, accurate for large-scale systems of small devices. Hence, in this work, we study population protocols in a setting where up to $f$ nodes can be Byzantine. We examine the majority (binary) consensus problem against different levels of adversary strengths, ranging from the Full Byzantine adversary that has complete knowledge of all the node states to the Weak Content-Oblivious Byzantine adversary that has only knowledge about which exchanges take place. We also take into account Dynamic vs Static node corruption by the adversary. We give lower bounds that require any algorithm solving the majority consensus to have initial difference $d = \Omega(f + 1)$ for the tally between the two proposed values, which holds for both the Full Static and Weak Dynamic adversaries. We then present an algorithm that solves the majority consensus problem and tolerates $f \leq n / c$ Byzantine nodes, for some constant $c>0$, with $d = \Omega(f + \sqrt{n \log n})$ and $O(\log^3 n)$ parallel time steps, using $O(\log^3 n)$ states per node. We also give an alternative algorithm, with the same asymptotic performance, for $d = \Omega(\min\{f \log^2 n + 1,n\})$. Finally, we combine both algorithms into one using a new robust distributed common coin. The only other known previous work on Byzantine-resilient population protocols tolerates up to $f = o(\sqrt n)$ faulty nodes and was analyzed against a Static adversary; hence, our protocols significantly improve fault-tolerance by an $\omega(\sqrt n)$ factor and all of them work correctly against a stronger Dynamic adversary.

cs.DC↗

arXiv2020

The Hermes BFT for Blockchains

The performance of partially synchronous BFT-based consensus protocols is highly dependent on the primary node. All participant nodes in the network are blocked until they receive a proposal from the primary node to begin the consensus process.Therefore, an honest but slack node (with limited bandwidth) can adversely affect the performance when selected as primary. Hermes decreases protocol dependency on the primary node and minimizes transmission delay induced by the slack primary while keeping low message complexity and latency. Hermes achieves these performance improvements by relaxing strong BFT agreement (safety) guarantees only for a specific type of Byzantine faults (also called equivocated faults). Interestingly, we show that in Hermes equivocating by a Byzantine primary is unlikely, expensive and ineffective. Therefore, the safety of Hermes is comparable to the general BFT consensus. We deployed and tested Hermes on 190 Amazon EC2 instances. In these tests, Hermes's performance was comparable to the state-of-the-art BFT protocol for blockchains (when the network size is large) in the absence of slack nodes. Whereas, in the presence of slack nodes Hermes out performed the state-of-the-art BFT protocol by more than 4x in terms of throughput as well as 15x in terms of latency.

cs.DC↗

arXiv2019

Window Based BFT Blockchain Consensus

There is surge of interest to the blockchain technology not only in the scientific community but in the business community as well. Proof of Work (PoW) and Byzantine Fault Tolerant (BFT) are the two main classes of consensus protocols that are used in the blockchain consensus layer. PoW is highly scalable but very slow with about 7 (transactions/second) performance. BFT based protocols are highly efficient but their scalability are limited to only tens of nodes. One of the main reasons for the BFT limitation is the quadratic $O(n^2)$ communication complexity of BFT based protocols for $n$ nodes that requires $n \times n$ broadcasting. In this paper, we present the {\em Musch} protocol which is BFT based and provides communication complexity $O(f n + n)$ for $f$ failures and $n$ nodes, where $f < n/3$, without compromising the latency. Hence, the performance adjusts to $f$ such that for constant $f$ the communication complexity is linear. Musch achieves this by introducing the notion of exponentially increasing windows of nodes to which complains are reported, instead of broadcasting to all the nodes. To our knowledge, this is the first BFT-based blockchain protocol which efficiently addresses simultaneously the issues of communication complexity and latency under the presence of failures.

cs.DC↗

arXiv2019

Proteus: A Scalable BFT Consesus Protocol for Blockchains

Byzantine Fault Tolerant (BFT) consensus exhibits higher throughput in comparison to Proof of Work (PoW) in blockchains. But BFT-based protocols suffer from scalability problems with respect to the number of replicas in the network. The main reason for this limitation is the quadratic message complexity of BFT protocols. Previously, proposed solutions improve BFT performance for normal operation, but will fall back to quadratic message complexity once the protocol observes a certain number of failures. This makes the protocol performance unpredictable as it is not guaranteed that the network will face a a certain number of failures. As a result, such protocols are only scalable when conditions are favorable (i.e., the number of failures are less than a given threshold). To address this issue we propose Proteus, a new BFT-based consensus protocol which elects a subset of nodes $c$ as a root committee. Proteus guarantees stable performance, regardless of the number of failures in the network and it improves on the quadratic message complexity of typical BFT-based protocols to $O(cn)$, where $c<<n$, for large $n$. Thus, message complexity remains small and less than quadratic when $c$ is asymptotically smaller than $n$, and this helps the protocol to provide stable performance even during the view change process (change of root committee). Our view change process is different than typical BFT protocols as it replaces the whole root committee compared to replacing a single primary in other protocols. We deployed and tested our protocol on $200$ Amazon $EC2$ instances, with two different baseline BFT protocols (PBFT and Bchain) for comparison. In these tests, our protocol outperformed the baselines by more than $2\times$ in terms of throughput as well as latency.

cs.DC↗

arXiv2015

On Strong Graph Partitions and Universal Steiner Trees

We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph $G$ and a root node $r$, we seek a single spanning tree $T$ of minimum {\em stretch}, where the stretch of $T$ is defined to be the maximum ratio, over all terminal sets $X$, of the cost of the minimal sub-tree $T_X$ of $T$ that connects $X$ to $r$ to the cost of an optimal Steiner tree connecting $X$ to $r$ in $G$. Universal Steiner trees (USTs) are important for data aggregation problems where computing the Steiner tree from scratch for every input instance of terminals is costly, as for example in low energy sensor network applications. We provide a polynomial time \ust\ construction for general graphs with $2^{O(\sqrt{\log n})}$-stretch. We also give a polynomial time $\polylog(n)$-stretch construction for minor-free graphs. One basic building block of our algorithms is a hierarchy of graph partitions, each of which guarantees small strong diameter for each cluster and bounded neighbourhood intersections for each node. We show close connections between the problems of constructing USTs and building such graph partitions. Our construction of partition hierarchies for general graphs is based on an iterative cluster merging procedure, while the one for minor-free graphs is based on a separator theorem for such graphs and the solution to a cluster aggregation problem that may be of independent interest even for general graphs. To our knowledge, this is the first subpolynomial-stretch ($o(n^ε)$ for any $ε> 0$) UST construction for general graphs, and the first polylogarithmic-stretch UST construction for minor-free graphs.

cs.DS↗

arXiv2013

Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors are for the current round before they broadcast their messages. Queue requests may arrive over rounds at arbitrary nodes and the goal is to eventually enqueue them in a distributed queue. We present two algorithms that give a total distributed ordering of queue requests in this model. We measure the performance of our algorithms through round complexity, which is the total number of rounds needed to solve the distributed queuing problem. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk) rounds using O(log n) size messages, where n is the number of nodes in the network and k <= n is the number of queue requests. Further, we show that for more stable graphs, e.g. T-interval connected graphs where the communication links change in every T rounds, the distributed queuing problem can be solved in O(n+ (nk/min(alpha,T))) rounds using the same O(log n) size messages, where alpha > 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system in any round. These results hold in any arbitrary (sequential, one-shot concurrent, or dynamic) arrival of k queue requests in the system. Moreover, our algorithms ensure correctness in the sense that each queue request is eventually enqueued in the distributed queue after it is issued and each queue request is enqueued exactly once. We also provide an impossibility result for this distributed queuing problem in this model. To the best of our knowledge, these are the first solutions to the distributed queuing problem in adversarial dynamic networks.

cs.DC↗

arXiv2013

The Price of Anarchy is Unbounded for Congestion Games with Superpolynomial Latency Costs

We consider non-cooperative unsplittable congestion games where players share resources, and each player's strategy is pure and consists of a subset of the resources on which it applies a fixed weight. Such games represent unsplittable routing flow games and also job allocation games. The congestion of a resource is the sum of the weights of the players that use it and the player's cost function is the sum of the utilities of the resources on its strategy. The social cost is the total weighted sum of the player's costs. The quality of Nash equilibria is determined by the price of anarchy ($PoA$) which expresses how much worse is the social outcome in the worst equilibrium versus the optimal coordinated solution. In the literature the predominant work has only been on games with polynomial utility costs, where it has been proven that the price of anarchy is bounded by the degree of the polynomial. However, no results exist on general bounds for non-polynomial utility functions. Here, we consider general versions of these games in which the utility of each resource is an arbitrary non-decreasing function of the congestion. In particular, we consider a large family of superpolynomial utility functions which are asymptotically larger than any polynomial. We demonstrate that for every such function there exist games for which the price of anarchy is unbounded and increasing with the number of players (even if they have infinitesimal weights) while network resources remain fixed. We give tight lower and upper bounds which show this dependence on the number of players. Furthermore we provide an exact characterization of the $PoA$ of all congestion games whose utility costs are bounded above by a polynomial function. Heretofore such results existed only for games with polynomial cost functions.

cs.GT↗

arXiv2010

A Streaming Approximation Algorithm for Klee's Measure Problem

The efficient estimation of frequency moments of a data stream in one-pass using limited space and time per item is one of the most fundamental problem in data stream processing. An especially important estimation is to find the number of distinct elements in a data stream, which is generally referred to as the zeroth frequency moment and denoted by $F_0$. In this paper, we consider streams of rectangles defined over a discrete space and the task is to compute the total number of distinct points covered by the rectangles. This is known as the Klee's measure problem in 2 dimensions. We present and analyze a randomized streaming approximation algorithm which gives an $(ε, δ)$-approximation of $F_0$ for the total area of Klee's measure problem in 2 dimensions. Our algorithm achieves the following complexity bounds: (a) the amortized processing time per rectangle is $O(\frac{1}{ε^4}\log^3 n\log\frac{1}δ)$; (b) the space complexity is $O(\frac{1}{ε^2}\log n \log\frac{1}δ)$ bits; and (c) the time to answer a query for $F_0$ is $O(\log\frac{1}δ)$, respectively. To our knowledge, this is the first streaming approximation for the Klee's measure problem that achieves sub-polynomial bounds.

cs.DS↗

arXiv2010

Polynomial Bottleneck Congestion Games with Optimal Price of Anarchy

We study {\em bottleneck congestion games} where the social cost is determined by the worst congestion of any resource. These games directly relate to network routing problems and also job-shop scheduling problems. In typical bottleneck congestion games, the utility costs of the players are determined by the worst congested resources that they use. However, the resulting Nash equilibria are inefficient, since the price of anarchy is proportional on the number of resources which can be high. Here we show that we can get smaller price of anarchy with the bottleneck social cost metric. We introduce the {\em polynomial bottleneck games} where the utility costs of the players are polynomial functions of the congestion of the resources that they use. In particular, the delay function for any resource $r$ is $C_{r}^\M$, where $C_r$ is the congestion measured as the number of players that use $r$, and $\M \geq 1$ is an integer constant that defines the degree of the polynomial. The utility cost of a player is the sum of the individual delays of the resources that it uses. The social cost of the game remains the same, namely, it is the worst bottleneck resource congestion: $\max_{r} C_r$. We show that polynomial bottleneck games are very efficient and give price of anarchy $O(|R|^{1/(\M+1)})$, where $R$ is the set of resources. This price of anarchy is tight, since we demonstrate a game with price of anarchy $Ω(|R|^{1/(\M+1)})$, for any $\M \geq 1$. We obtain our tight bounds by using two proof techniques: {\em transformation}, which we use to convert arbitrary games to simpler games, and {\em expansion}, which we use to bound the price of anarchy in a simpler game.

cs.GT↗