821 research outputs found
Improved Bi-criteria Approximation for the All-or-Nothing Multicommodity Flow Problem in Arbitrary Networks
This paper addresses the following fundamental maximum throughput routing
problem: Given an arbitrary edge-capacitated -node directed network and a
set of commodities, with source-destination pairs and demands
, admit and route the largest possible number of commodities -- i.e.,
the maximum {\em throughput} -- to satisfy their demands. The main
contributions of this paper are two-fold: First, we present a bi-criteria
approximation algorithm for this all-or-nothing multicommodity flow (ANF)
problem. Our algorithm is the first to achieve a {\em constant approximation of
the maximum throughput} with an {\em edge capacity violation ratio that is at
most logarithmic in }, with high probability. Our approach is based on a
version of randomized rounding that keeps splittable flows, rather than
approximating those via a non-splittable path for each commodity: This allows
our approach to work for {\em arbitrary directed edge-capacitated graphs},
unlike most of the prior work on the ANF problem. Our algorithm also works if
we consider the weighted throughput, where the benefit gained by fully
satisfying the demand for commodity is determined by a given weight
. Second, we present a derandomization of our algorithm that maintains
the same approximation bounds, using novel pessimistic estimators for
Bernstein's inequality. In addition, we show how our framework can be adapted
to achieve a polylogarithmic fraction of the maximum throughput while
maintaining a constant edge capacity violation, if the network capacity is
large enough. One important aspect of our randomized and derandomized
algorithms is their {\em simplicity}, which lends to efficient implementations
in practice
Thresholded Covering Algorithms for Robust and Max-Min Optimization
The general problem of robust optimization is this: one of several possible
scenarios will appear tomorrow, but things are more expensive tomorrow than
they are today. What should you anticipatorily buy today, so that the
worst-case cost (summed over both days) is minimized? Feige et al. and
Khandekar et al. considered the k-robust model where the possible outcomes
tomorrow are given by all demand-subsets of size k, and gave algorithms for the
set cover problem, and the Steiner tree and facility location problems in this
model, respectively.
In this paper, we give the following simple and intuitive template for
k-robust problems: "having built some anticipatory solution, if there exists a
single demand whose augmentation cost is larger than some threshold, augment
the anticipatory solution to cover this demand as well, and repeat". In this
paper we show that this template gives us improved approximation algorithms for
k-robust Steiner tree and set cover, and the first approximation algorithms for
k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios
(except for multicut) are almost best possible.
As a by-product of our techniques, we also get algorithms for max-min
problems of the form: "given a covering problem instance, which k of the
elements are costliest to cover?".Comment: 24 page
Structural Routability of n-Pairs Information Networks
Information does not generally behave like a conservative fluid flow in
communication networks with multiple sources and sinks. However, it is often
conceptually and practically useful to be able to associate separate data
streams with each source-sink pair, with only routing and no coding performed
at the network nodes. This raises the question of whether there is a nontrivial
class of network topologies for which achievability is always equivalent to
routability, for any combination of source signals and positive channel
capacities. This chapter considers possibly cyclic, directed, errorless
networks with n source-sink pairs and mutually independent source signals. The
concept of downward dominance is introduced and it is shown that, if the
network topology is downward dominated, then the achievability of a given
combination of source signals and channel capacities implies the existence of a
feasible multicommodity flow.Comment: The final publication is available at link.springer.com
http://link.springer.com/chapter/10.1007/978-3-319-02150-8_
On Routing Disjoint Paths in Bounded Treewidth Graphs
We study the problem of routing on disjoint paths in bounded treewidth graphs
with both edge and node capacities. The input consists of a capacitated graph
and a collection of source-destination pairs . The goal is to maximize the number of pairs that
can be routed subject to the capacities in the graph. A routing of a subset
of the pairs is a collection of paths such that,
for each pair , there is a path in
connecting to . In the Maximum Edge Disjoint Paths (MaxEDP) problem,
the graph has capacities on the edges and a routing
is feasible if each edge is in at most of
the paths of . The Maximum Node Disjoint Paths (MaxNDP) problem is
the node-capacitated counterpart of MaxEDP.
In this paper we obtain an approximation for MaxEDP on graphs of
treewidth at most and a matching approximation for MaxNDP on graphs of
pathwidth at most . Our results build on and significantly improve the work
by Chekuri et al. [ICALP 2013] who obtained an approximation
for MaxEDP
Towards random uniform sampling of bipartite graphs with given degree sequence
In this paper we consider a simple Markov chain for bipartite graphs with
given degree sequence on vertices. We show that the mixing time of this
Markov chain is bounded above by a polynomial in in case of {\em
semi-regular} degree sequence. The novelty of our approach lays in the
construction of the canonical paths in Sinclair's method.Comment: 47 pages, submitted for publication. In this version we explain
explicitly our main contribution and corrected a serious flaw in the cycle
decompositio
Graph Orientation and Flows Over Time
Flows over time are used to model many real-world logistic and routing
problems. The networks underlying such problems -- streets, tracks, etc. -- are
inherently undirected and directions are only imposed on them to reduce the
danger of colliding vehicles and similar problems. Thus the question arises,
what influence the orientation of the network has on the network flow over time
problem that is being solved on the oriented network. In the literature, this
is also referred to as the contraflow or lane reversal problem.
We introduce and analyze the price of orientation: How much flow is lost in
any orientation of the network if the time horizon remains fixed? We prove that
there is always an orientation where we can still send of the
flow and this bound is tight. For the special case of networks with a single
source or sink, this fraction is which is again tight. We present
more results of similar flavor and also show non-approximability results for
finding the best orientation for single and multicommodity maximum flows over
time
Compact Oblivious Routing
Oblivious routing is an attractive paradigm for large distributed systems in which centralized control and frequent reconfigurations are infeasible or undesired (e.g., costly). Over the last almost 20 years, much progress has been made in devising oblivious routing schemes that guarantee close to optimal load and also algorithms for constructing such schemes efficiently have been designed. However, a common drawback of existing oblivious routing schemes is that they are not compact: they require large routing tables (of polynomial size), which does not scale.
This paper presents the first oblivious routing scheme which guarantees close to optimal load and is compact at the same time - requiring routing tables of polylogarithmic size. Our algorithm maintains the polylogarithmic competitive ratio of existing algorithms, and is hence particularly well-suited for emerging large-scale networks
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