4 research outputs found
Serving Online Requests with Mobile Servers
We study an online problem in which a set of mobile servers have to be moved
in order to efficiently serve a set of requests that arrive in an online
fashion. More formally, there is a set of nodes and a set of mobile
servers that are placed at some of the nodes. Each node can potentially host
several servers and the servers can be moved between the nodes. There are
requests that are adversarially issued at nodes one at a time. An
issued request at time needs to be served at all times . The
cost for serving the requests is a function of the number of servers and
requests at the different nodes. The requirements on how to serve the requests
are governed by two parameters and . An algorithm
needs to guarantee at all times that the total service cost remains within a
multiplicative factor of and an additive term of the current
optimal service cost. We consider online algorithms for two different
minimization objectives. We first consider the natural problem of minimizing
the total number of server movements. We show that in this case for every ,
the competitive ratio of every deterministic online algorithm needs to be at
least . Given this negative result, we then extend the minimization
objective to also include the current service cost. We give almost tight bounds
on the competitive ratio of the online problem where one needs to minimize the
sum of the total number of movements and the current service cost. In
particular, we show that at the cost of an additional additive term which is
roughly linear in , it is possible to achieve a multiplicative competitive
ratio of for every constant .Comment: 25 page
Dynamic Analysis of the Arrow Distributed Directory Protocol in General Networks
The Arrow protocol is a simple and elegant protocol to coordinate exclusive access to a shared object in a network. The protocol solves the underlying distributed queueing problem by using path reversal on a pre-computed spanning tree (or any other tree topology simulated on top of the given network).
It is known that the Arrow protocol solves the problem with a competitive ratio of O(log D) on trees of diameter D. This implies a distributed queueing algorithm with competitive ratio O(s log D) for general networks with a spanning tree of diameter D and stretch s. In this work we show that when running the Arrow protocol on top of the well-known probabilistic tree embedding of Fakcharoenphol, Rao, and Talwar [STOC\u2703], we obtain a randomized distributed online queueing algorithm with expected competitive ratio O(log n) against an oblivious adversary even on general n-node network topologies. The result holds even if the queueing requests occur in an arbitrarily dynamic and concurrent fashion and even if communication is asynchronous. The main technical result of the paper shows that the competitive ratio of the Arrow protocol is constant on a special family of tree topologies, known as hierarchically well separated trees
The Cost of Global Broadcast in Dynamic Radio Networks
We study the single-message broadcast problem in dynamic radio networks. We
show that the time complexity of the problem depends on the amount of stability
and connectivity of the dynamic network topology and on the adaptiveness of the
adversary providing the dynamic topology. More formally, we model communication
using the standard graph-based radio network model. To model the dynamic
network, we use a generalization of the synchronous dynamic graph model
introduced in [Kuhn et al., STOC 2010]. For integer parameters and
, we call a dynamic graph -interval -connected if for every
interval of consecutive rounds, there exists a -vertex-connected stable
subgraph. Further, for an integer parameter , we say that the
adversary providing the dynamic network is -oblivious if for constructing
the graph of some round , the adversary has access to all the randomness
(and states) of the algorithm up to round .
As our main result, we show that for any , any , and any
, for a -oblivious adversary, there is a distributed
algorithm to broadcast a single message in time
. We further show that even for large interval -connectivity,
efficient broadcast is not possible for the usual adaptive adversaries. For a
-oblivious adversary, we show that even for any (for any constant ) and for any , global broadcast in -interval -connected networks requires at least
time. Further, for a oblivious adversary,
broadcast cannot be solved in -interval -connected networks as long as
.Comment: 17 pages, conference version appeared in OPODIS 201
Concurrent Distributed Serving with Mobile Servers
This paper introduces a new resource allocation problem in distributed computing called distributed serving with mobile servers (DSMS). In DSMS, there are k identical mobile servers residing at the processors of a network. At arbitrary points of time, any subset of processors can invoke one or more requests. To serve a request, one of the servers must move to the processor that invoked the request. Resource allocation is performed in a distributed manner since only the processor that invoked the request initially knows about it. All processors cooperate by passing messages to achieve correct resource allocation. They do this with the goal to minimize the communication cost.
Routing servers in large-scale distributed systems requires a scalable location service. We introduce the distributed protocol Gnn that solves the DSMS problem on overlay trees. We prove that Gnn is starvation-free and correctly integrates locating the servers and synchronizing the concurrent access to servers despite asynchrony, even when the requests are invoked over time. Further, we analyze Gnn for "one-shot" executions, i.e., all requests are invoked simultaneously. We prove that when running Gnn on top of a special family of tree topologies - known as hierarchically well-separated trees (HSTs) - we obtain a randomized distributed protocol with an expected competitive ratio of O(log n) on general network topologies with n processors. From a technical point of view, our main result is that Gnn optimally solves the DSMS problem on HSTs for one-shot executions, even if communication is asynchronous. Further, we present a lower bound of Omega(max {k, log n/log log n}) on the competitive ratio for DSMS. The lower bound even holds when communication is synchronous and requests are invoked sequentially