12 research outputs found
Approximation Algorithms for Covering/Packing Integer Programs
Given matrices A and B and vectors a, b, c and d, all with non-negative
entries, we consider the problem of computing min {c.x: x in Z^n_+, Ax > a, Bx
< b, x < d}. We give a bicriteria-approximation algorithm that, given epsilon
in (0, 1], finds a solution of cost O(ln(m)/epsilon^2) times optimal, meeting
the covering constraints (Ax > a) and multiplicity constraints (x < d), and
satisfying Bx < (1 + epsilon)b + beta, where beta is the vector of row sums
beta_i = sum_j B_ij. Here m denotes the number of rows of A.
This gives an O(ln m)-approximation algorithm for CIP -- minimum-cost
covering integer programs with multiplicity constraints, i.e., the special case
when there are no packing constraints Bx < b. The previous best approximation
ratio has been O(ln(max_j sum_i A_ij)) since 1982. CIP contains the set cover
problem as a special case, so O(ln m)-approximation is the best possible unless
P=NP.Comment: Preliminary version appeared in IEEE Symposium on Foundations of
Computer Science (2001). To appear in Journal of Computer and System Science
Asymptotically Optimal Approximation Algorithms for Coflow Scheduling
Many modern datacenter applications involve large-scale computations composed
of multiple data flows that need to be completed over a shared set of
distributed resources. Such a computation completes when all of its flows
complete. A useful abstraction for modeling such scenarios is a {\em coflow},
which is a collection of flows (e.g., tasks, packets, data transmissions) that
all share the same performance goal.
In this paper, we present the first approximation algorithms for scheduling
coflows over general network topologies with the objective of minimizing total
weighted completion time. We consider two different models for coflows based on
the nature of individual flows: circuits, and packets. We design
constant-factor polynomial-time approximation algorithms for scheduling
packet-based coflows with or without given flow paths, and circuit-based
coflows with given flow paths. Furthermore, we give an -approximation polynomial time algorithm for scheduling circuit-based
coflows where flow paths are not given (here is the number of network
edges).
We obtain our results by developing a general framework for coflow schedules,
based on interval-indexed linear programs, which may extend to other coflow
models and objective functions and may also yield improved approximation bounds
for specific network scenarios. We also present an experimental evaluation of
our approach for circuit-based coflows that show a performance improvement of
at least 22% on average over competing heuristics.Comment: Fixed minor typo
Packet Forwarding Algorithms in a Line Network
Abstract. We initiate a competitive analysis of packet forwarding poli-cies for maximum and average flow in a line network. We show that the policies Earliest Arrival and Furthest-To-Go are scalable, but not con-stant competitive, for maximum flow. We show that there is no constant competitive algorithm for average flow.
Hop-Constrained Oblivious Routing
We prove the existence of an oblivious routing scheme that is
-competitive in terms of , thus
resolving a well-known question in oblivious routing.
Concretely, consider an undirected network and a set of packets each with its
own source and destination. The objective is to choose a path for each packet,
from its source to its destination, so as to minimize , defined as follows: The dilation is the maximum path hop-length,
and the congestion is the maximum number of paths that include any single edge.
The routing scheme obliviously and randomly selects a path for each packet
independent of (the existence of) the other packets. Despite this
obliviousness, the selected paths have within a
factor of the best possible value. More precisely, for
any integer hop-bound , this oblivious routing scheme selects paths of
length at most and is -competitive in terms of in comparison to the best possible
achievable via paths of length at most hops. These paths can
be sampled in polynomial time.
This result can be viewed as an analogue of the celebrated oblivious routing
results of R\"{a}cke [FOCS 2002, STOC 2008], which are -competitive
in terms of , but are not competitive in terms of
A constant-factor approximation algorithm for packet routing and balancing local vs. global criteria
SIAM Journal on Computing3062051-2068SMJC