arXiv subjects

Seth Gilbert

Publications and source records attributed to Seth Gilbert.

41 records · Page 3Linked to original sources

arXiv2015

Smoothed Analysis of Dynamic Networks

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, dynamic graph smoothed analysis studies the impact of random perturbations of the underlying changing network graph topologies. Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in dynamic network models are robust or fragile: do they withstand small (random) perturbations, or do such deviations push the graphs far enough from a precise pathological instance to enable much better performance? Fragile lower bounds are likely not relevant for real-world deployment, while robust lower bounds represent a true difficulty caused by dynamic behavior. We apply this technique to three standard dynamic network problems with known strong worst-case lower bounds: random walks, flooding, and aggregation. We prove that these bounds provide a spectrum of robustness when subjected to smoothing---some are extremely fragile (random walks), some are moderately fragile / robust (flooding), and some are extremely robust (aggregation).

cs.DC↗

arXiv2015

How to Scale Exponential Backoff

Randomized exponential backoff is a widely deployed technique for coordinating access to a shared resource. A good backoff protocol should, arguably, satisfy three natural properties: (i) it should provide constant throughput, wasting as little time as possible; (ii) it should require few failed access attempts, minimizing the amount of wasted effort; and (iii) it should be robust, continuing to work efficiently even if some of the access attempts fail for spurious reasons. Unfortunately, exponential backoff has some well-known limitations in two of these areas: it provides poor (sub-constant) throughput (in the worst case), and is not robust (to resource acquisition failures). The goal of this paper is to "fix" exponential backoff by making it scalable, particularly focusing on the case where processes arrive in an on-line, worst-case fashion. We present a relatively simple backoff protocol~Re-Backoff~that has, at its heart, a version of exponential backoff. It guarantees expected constant throughput with dynamic process arrivals and requires only an expected polylogarithmic number of access attempts per process. Re-Backoff is also robust to periods where the shared resource is unavailable for a period of time. If it is unavailable for $D$ time slots, Re-Backoff provides the following guarantees. When the number of packets is a finite $n$, the average expected number of access attempts for successfully sending a packet is $O(\log^2( n + D))$. In the infinite case, the average expected number of access attempts for successfully sending a packet is $O( \log^2(η) + \log^2(D) )$ where $η$ is the maximum number of processes that are ever in the system concurrently.

cs.DC↗

arXiv2013

Reallocation Problems in Scheduling

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a sufficiently feasible schedule exists. The algorithm reschedules only a total number of O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from the system, where n is the number of active jobs and Delta is the size of the largest window.

cs.DS↗

arXiv2012

Making Evildoers Pay: Resource-Competitive Broadcast in Sensor Networks

Consider a time-slotted, single-hop, wireless sensor network (WSN) consisting of n correct devices and and t=f*n Byzantine devices where f>=0 is any constant; that is, the Byzantine devices may outnumber the correct ones. There exists a trusted sender Alice who wishes to deliver a message m over a single channel to the correct devices. There also exists a malicious user Carol who controls the t Byzantine devices and uses them to disrupt the communication channel. For a constant k>=2, the correct and Byzantine devices each possess a meager energy budget of O(n^{1/k}), Alice and Carol each possess a limited budget of \tilde{O}(n^{1/k}), and sending or listening in a slot incurs unit cost. This general setup captures the inherent challenges of guaranteeing communication despite scarce resources and attacks on the network. Given this Alice versus Carol scenario, we ask: Is communication of m feasible and, if so, at what cost? We develop a protocol which, for an arbitrarily small constant ε>0, ensures that at least (1-ε)n correct devices receive m with high probability. Furthermore, if Carol's devices expend T energy jamming the channel, then Alice and the correct devices each spend only \tilde{O}(T^{1/(k+1)}). In other words, delaying the transmission of m forces a jammer to rapidly deplete its energy supply and, consequently, cease attacks on the network.

cs.DC↗

arXiv2011

A New Approach to Incremental Cycle Detection and Related Problems

We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two algorithms, one suited to sparse graphs, and the other to dense graphs. The former takes the minimum of O(m^{3/2}) and O(mn^{2/3}) time to insert m arcs into an n-vertex graph; the latter takes O(n^2 log(n)) time. Our sparse algorithm is considerably simpler than a previous O(m^{3/2})-time algorithm; it is also faster on graphs of sufficient density. The time bound of our dense algorithm beats the previously best time bound of O(n^{5/2}) for dense graphs. Our algorithms rely for their efficiency on topologically ordered vertex numberings; bounds on the size of the numbers give bound on running times.

cs.DS↗