52 research outputs found
The Knapsack Problem with Neighbour Constraints
We study a constrained version of the knapsack problem in which dependencies
between items are given by the adjacencies of a graph. In the 1-neighbour
knapsack problem, an item can be selected only if at least one of its
neighbours is also selected. In the all-neighbours knapsack problem, an item
can be selected only if all its neighbours are also selected. We give
approximation algorithms and hardness results when the nodes have both uniform
and arbitrary weight and profit functions, and when the dependency graph is
directed and undirected.Comment: Full version of IWOCA 2011 pape
Routing Regardless of Network Stability
We examine the effectiveness of packet routing in this model for the broad
class next-hop preferences with filtering. Here each node v has a filtering
list D(v) consisting of nodes it does not want its packets to route through.
Acceptable paths (those that avoid nodes in the filtering list) are ranked
according to the next-hop, that is, the neighbour of v that the path begins
with. On the negative side, we present a strong inapproximability result. For
filtering lists of cardinality at most one, given a network in which an
equilibrium is guaranteed to exist, it is NP-hard to approximate the maximum
number of packets that can be routed to within a factor of O(n^{1-\epsilon}),
for any constant \epsilon >0. On the positive side, we give algorithms to show
that in two fundamental cases every packet will eventually route with
probability one. The first case is when each node's filtering list contains
only itself, that is, D(v)={v}. Moreover, with positive probability every
packet will be routed before the control plane reaches an equilibrium. The
second case is when all the filtering lists are empty, that is,
. Thus, with probability one packets will route even
when the nodes don't care if their packets cycle! Furthermore, with probability
one every packet will route even when the control plane has em no equilibrium
at all.Comment: ESA 201
Designing multihop wireless backhaul networks with delay guarantees
Abstract — As wireless access technologies improve in data rates, the problem focus is shifting towards providing adequate backhaul from the wireless access points to the Internet. Existing wired backhaul technologies such as copper wires running at DSL, T1, or T3 speeds can be expensive to install or lease, and are becoming a performance bottleneck as wireless access speeds increase. Longhaul, non-line-of-sight wireless technologies such as WiMAX (802.16d) hold the promise of enabling a high speed wireless backhaul as a cost-effective alternative. However, the biggest challenge in building a wireless backhaul is achieving guaranteed performance (throughput and delay) that is typically provided by a wired backhaul. This paper explores the problem of efficiently designing a multihop wireless backhaul to connect multiple wireless access points to a wired gateway. In particular, we provide a generalized link activation framework for scheduling packets over this wireless backhaul, such that any existing wireline scheduling policy can be implemented locally at each node of the wireless backhaul. We also present techniques for determining good interference-free routes within our scheduling framework, given the link rates and cross-link interference information. When a multihop wireline scheduler with worst case delay bounds (such as WFQ or Coordinated EDF) is implemented over the wireless backhaul, we show that our scheduling and routing framework guarantees approximately twice the delay of the corresponding wireline topology. Finally, we present simulation results to demonstrate the low delays achieved using our framework. I
Improving Robustness of Next-Hop Routing
A weakness of next-hop routing is that following a link or router failure
there may be no routes between some source-destination pairs, or packets may
get stuck in a routing loop as the protocol operates to establish new routes.
In this article, we address these weaknesses by describing mechanisms to choose
alternate next hops.
Our first contribution is to model the scenario as the following {\sc tree
augmentation} problem. Consider a mixed graph where some edges are directed and
some undirected. The directed edges form a spanning tree pointing towards the
common destination node. Each directed edge represents the unique next hop in
the routing protocol. Our goal is to direct the undirected edges so that the
resulting graph remains acyclic and the number of nodes with outdegree two or
more is maximized. These nodes represent those with alternative next hops in
their routing paths.
We show that {\sc tree augmentation} is NP-hard in general and present a
simple -approximation algorithm. We also study 3 special cases. We
give exact polynomial-time algorithms for when the input spanning tree consists
of exactly 2 directed paths or when the input graph has bounded treewidth. For
planar graphs, we present a polynomial-time approximation scheme when the input
tree is a breadth-first search tree. To the best of our knowledge, {\sc tree
augmentation} has not been previously studied
Overlaying Circuit Clauses for Secure Computation
Given a set S = {C_1,...,C_k } of Boolean circuits, we show how to construct a universal for S circuit C_0, which is much smaller than Valiant’s universal circuit or a circuit incorporating all C_1,...,C_k. Namely, given C_1,...,C_k and viewing them as directed acyclic graphs (DAGs) D_1,...,D_k, we embed them in a new graph D_0. The embedding is such that a GC garbling of any of C_1,...,C_k could be implemented by a corresponding garbling of a circuit corresponding to D_0.
We show how to improve Garbled Circuit (GC) and GMW-based secure function evaluation (SFE) of circuits with if/switch clauses using such S-universal circuit.
The most interesting case here is the application to the GMW approach. We provide a novel observation that in GMW the cost of processing a gate is almost the same for 5 (or more) Boolean inputs,
as it is for the usual case of 2 Boolean inputs. While we expect this observation to greatly improve general GMW-based computation, in our context this means that GMW gates can be programmed almost for free, based on the secret-shared programming of the clause.
Our approach naturally and cheaply supports nested clauses. Our algorithm is a heuristic; we show that solving the circuit embedding problem is NP-hard. Our algorithms are in the semi-honest model and are compatible with Free-XOR.
We report on experimental evaluations and discuss achieved performance in detail. For 32 diverse circuits in our experiment, our construction results 6.1x smaller circuit than prior techniques
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