367 research outputs found
Power Aware Routing for Sensor Databases
Wireless sensor networks offer the potential to span and monitor large
geographical areas inexpensively. Sensor network databases like TinyDB are the
dominant architectures to extract and manage data in such networks. Since
sensors have significant power constraints (battery life), and high
communication costs, design of energy efficient communication algorithms is of
great importance. The data flow in a sensor database is very different from
data flow in an ordinary network and poses novel challenges in designing
efficient routing algorithms. In this work we explore the problem of energy
efficient routing for various different types of database queries and show that
in general, this problem is NP-complete. We give a constant factor
approximation algorithm for one class of query, and for other queries give
heuristic algorithms. We evaluate the efficiency of the proposed algorithms by
simulation and demonstrate their near optimal performance for various network
sizes
A Polyhedral Intersection Theorem for Capacitated Spanning Trees
In a two-capacitated spanning tree of a complete graph with a distinguished root vertex v, every component of the induced subgraph on V\{v} has at most two vertices. We give a complete,non-redundant characterization of the polytope defined by the convex hull of the incidence vectors of two-capacitated spanning trees. This polytope is the intersection of the spanning tree polytope on the given graph and the matching polytope on the subgraph induced by removing the root node and its incident edges. This result is one of very few known cases in which the intersection of two integer polyhedra yields another integer polyhedron. We also give a complete polyhedral characterization of a related polytope, the 2-capacitated forest polytope
Combinatorial Optimization
This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th
Throughput-Optimal Topology Design for Cross-Silo Federated Learning
NeurIPS 2020International audienceFederated learning usually employs a client-server architecture where an orchestrator iteratively aggregates model updates from remote clients and pushes them back a refined model. This approach may be inefficient in cross-silo settings, as close-by data silos with high-speed access links may exchange information faster than with the orchestrator, and the orchestrator may become a communication bottleneck. In this paper we define the problem of topology design for cross-silo federated learning using the theory of max-plus linear systems to compute the system throughput---number of communication rounds per time unit. We also propose practical algorithms that, under the knowledge of measurable network characteristics, find a topology with the largest throughput or with provable throughput guarantees. In realistic Internet networks with 10 Gbps access links for silos, our algorithms speed up training by a factor 9 and 1.5 in comparison to the master-slave architecture and to state-of-the-art MATCHA, respectively. Speedups are even larger with slower access links
The optimal location of facilities on a network
Imperial Users onl
Fast Augmenting Paths by Random Sampling from Residual Graphs
Consider an n-vertex, m-edge, undirected graph with integral capacities and max-flow value v. We give a new [~ over O](m + nv)-time maximum flow algorithm. After assigning certain special sampling probabilities to edges in [~ over O](m)$ time, our algorithm is very simple: repeatedly find an augmenting path in a random sample of edges from the residual graph. Breaking from past work, we demonstrate that we can benefit by random sampling from directed (residual) graphs. We also slightly improve an algorithm for approximating flows of arbitrary value, finding a flow of value (1 - ε) times the maximum in [~ over O](m√n/ε) time.National Science Foundation (U.S.
Faster Cut Sparsification of Weighted Graphs
A cut sparsifier is a reweighted subgraph that maintains the weights of the
cuts of the original graph up to a multiplicative factor of .
This paper considers computing cut sparsifiers of weighted graphs of size
. Our algorithm computes such a sparsifier in time
, both for graphs with polynomially
bounded and unbounded integer weights, where is the functional
inverse of Ackermann's function. This improves upon the state of the art by
Bencz\'ur and Karger (SICOMP 2015), which takes time. For
unbounded weights, this directly gives the best known result for cut
sparsification. Together with preprocessing by an algorithm of Fung et al.
(SICOMP 2019), this also gives the best known result for polynomially-weighted
graphs. Consequently, this implies the fastest approximate min-cut algorithm,
both for graphs with polynomial and unbounded weights. In particular, we show
that it is possible to adapt the state of the art algorithm of Fung et al. for
unweighted graphs to weighted graphs, by letting the partial maximum spanning
forest (MSF) packing take the place of the Nagamochi-Ibaraki (NI) forest
packing. MSF packings have previously been used by Abraham at al. (FOCS 2016)
in the dynamic setting, and are defined as follows: an -partial MSF packing
of is a set , where is a maximum
spanning forest in . Our method for
computing (a sufficient estimation of) the MSF packing is the bottleneck in the
running time of our sparsification algorithm.Comment: To be presented at the 49th EATCS International Colloquium on
Automata, Languages and Programming (ICALP 2022
Incremental Exact Min-Cut in Poly-logarithmic Amortized Update Time
We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with ~O(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtained by combining a recent sparsification technique of Kawarabayashi and Thorup [STOC 2015] and an exact incremental algorithm of Henzinger [J. of Algorithm 1997].
We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon^2) space Monte-Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithm maintains a (1+epsilon)-approximation to the minimum cut. The algorithm has ~O(1) amortized update-time and constant query-time
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