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Moti Medina

Publications and source records attributed to Moti Medina.

29 records · Page 2Linked to original sources
arXiv2015

Non-Local Probes Do Not Help with Graph Problems

This work bridges the gap between distributed and centralised models of computing in the context of sublinear-time graph algorithms. A priori, typical centralised models of computing (e.g., parallel decision trees or centralised local algorithms) seem to be much more powerful than distributed message-passing algorithms: centralised algorithms can directly probe any part of the input, while in distributed algorithms nodes can only communicate with their immediate neighbours. We show that for a large class of graph problems, this extra freedom does not help centralised algorithms at all: for example, efficient stateless deterministic centralised local algorithms can be simulated with efficient distributed message-passing algorithms. In particular, this enables us to transfer existing lower bound results from distributed algorithms to centralised local algorithms.

cs.DS↗
arXiv2015

Better Online Deterministic Packet Routing on Grids

We consider the following fundamental routing problem. An adversary inputs packets arbitrarily at sources, each packet with an arbitrary destination. Traffic is constrained by link capacities and buffer sizes, and packets may be dropped at any time. The goal of the routing algorithm is to maximize throughput, i.e., route as many packets as possible to their destination. Our main result is an $O\left(\log n\right)$-competitive deterministic algorithm for an $n$-node line network (i.e., $1$-dimensional grid), requiring only that buffers can store at least $5$ packets, and that links can deliver at least $5$ packets per step. We note that $O(\log n)$ is the best ratio known, even for randomized algorithms, even when allowed large buffers and wide links. The best previous deterministic algorithm for this problem with constant-size buffers and constant-capacity links was $O(\log^5 n)$-competitive. Our algorithm works like admission-control algorithms in the sense that if a packet is not dropped immediately upon arrival, then it is "accepted" and guaranteed to be delivered. We also show how to extend our algorithm to a polylog-competitive algorithm for any constant-dimension grid.

cs.DS↗
arXiv2014

Best of Two Local Models: Local Centralized and Local Distributed Algorithms

We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in $\log^* n$, where $n$ is the number of vertices of the input graph. The recursive centralized local improvement technique by Nguyen and Onak~\cite{onak2008} is employed to obtain an improved distributed approximation scheme for maximum (weighted) matching. The improvement is twofold: we reduce the number of rounds from $O(\log n)$ to $O(\log^*n)$ for a wide range of instances and, our algorithms are deterministic rather than randomized.

cs.DS↗
arXiv2014

Distributed Maximum Matching in Bounded Degree Graphs

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least $(1-\eps)$ times the optimal in $Δ^{O(1/\eps)} + O\left(\frac{1}{\eps^2}\right) \cdot\log^*(n)$ rounds where $n$ is the number of vertices in the graph and $Δ$ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least $(1-\eps)$ times the optimal in $\log(\min\{1/\wmin,n/\eps\})^{O(1/\eps)}\cdot(Δ^{O(1/\eps)}+\log^*(n))$ rounds for edge-weights in $[\wmin,1]$. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie~(SPAA 2008). For the unweighted case they give a randomized $(1-\eps)$-approximation algorithm that runs in $O((\log(n)) /\eps^3)$ rounds. For the weighted case they give a randomized $(1/2-\eps)$-approximation algorithm that runs in $O(\log(\eps^{-1}) \cdot \log(n))$ rounds. Hence, our results improve on the previous ones when the parameters $Δ$, $\eps$ and $\wmin$ are constants (where we reduce the number of runs from $O(\log(n))$ to $O(\log^*(n))$), and more generally when $Δ$, $1/\eps$ and $1/\wmin$ are sufficiently slowly increasing functions of $n$. Moreover, our algorithms are deterministic rather than randomized.

cs.DC↗
arXiv2014

Online Packet-Routing in Grids with Bounded Buffers

We present deterministic and randomized algorithms for the problem of online packet routing in grids in the competitive network throughput model \cite{AKOR}. In this model the network has nodes with bounded buffers and bounded link capacities. The goal in this model is to maximize the throughput, i.e., the number of delivered packets. Our deterministic algorithm is the first online algorithm with an $O\left(\log^{O(1)}(n)\right)$ competitive ratio for uni-directional grids (where $n$ denotes the size of the network). The deterministic online algorithm is centralized and handles packets with deadlines. This algorithm is applicable to various ranges of values of buffer sizes and communication link capacities. In particular, it holds for buffer size and communication link capacity in the range $[3 \ldots \log n]$. Our randomized algorithm achieves an expected competitive ratio of $O(\log n)$ for the uni-directional line. This algorithm is applicable to a wide range of buffer sizes and communication link capacities. In particular, it holds also for unit size buffers and unit capacity links. This algorithm improves the best previous $O(\log^2 n)$-competitive ratio of Azar and Zachut \cite{AZ}.

cs.DS↗
arXiv2012

Online Multi-Commodity Flow with High Demands

This paper deals with the problem of computing, in an online fashion, a maximum benefit multi-commodity flow (\ONMCF), where the flow demands may be bigger than the edge capacities of the network. We present an online, deterministic, centralized, all-or-nothing, bi-criteria algorithm. The competitive ratio of the algorithm is constant, and the algorithm augments the capacities by at most a logarithmic factor. The algorithm can handle two types of flow requests: (i) low demand requests that must be routed along a path, and (ii) high demand requests that may be routed using a multi-path flow. Two extensions are discussed: requests with known durations and machine scheduling.

cs.DS↗
arXiv2012

Improved Approximation for Orienting Mixed Graphs

An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that admit a directed source-target path. This problem has recently arisen in the study of biological networks, and it also has applications in communication networks. In this paper, we identify an interesting local-to-global orientation property. This property enables us to modify the best known algorithms for maximum mixed graph orientation and some of its special structured instances, due to Elberfeld et al. (CPM '11), and obtain improved approximation ratios. We further proceed by developing an algorithm that achieves an even better approximation guarantee for the general setting of the problem. Finally, we study several well-motivated variants of this orientation problem.

cs.DS↗
arXiv2012

Competitive and Deterministic Embeddings of Virtual Networks

Network virtualization is an important concept to overcome the ossification of today's Internet as it facilitates innovation also in the network core and as it promises a more efficient use of the given resources and infrastructure. Virtual networks (VNets) provide an abstraction of the physical network: multiple VNets may cohabit the same physical network, but can be based on completely different protocol stacks (also beyond IP). One of the main challenges in network virtualization is the efficient admission control and embedding of VNets. The demand for virtual networks (e.g., for a video conference) can be hard to predict, and once the request is accepted, the specification / QoS guarantees must be ensured throughout the VNet's lifetime. This requires an admission control algorithm which only selects high-benefit VNets in times of scarce resources, and an embedding algorithm which realizes the VNet in such a way that the likelihood that future requests can be embedded as well is maximized. This article describes a generic algorithm for the online VNet embedding problem which does not rely on any knowledge of the future VNet requests but whose performance is competitive to an optimal offline algorithm that has complete knowledge of the request sequence in advance: the so-called competitive ratio is, loosely speaking, logarithmic in the sum of the resources. Our algorithm is generic in the sense that it supports multiple traffic models, multiple routing models, and even allows for nonuniform benefits and durations of VNet requests.

cs.NI↗
arXiv2011

Multi-Hop Routing and Scheduling in Wireless Networks in the SINR model

We present an algorithm for multi-hop routing and scheduling of requests in wireless networks in the \sinr\ model. The goal of our algorithm is to maximize the throughput or maximize the minimum ratio between the flow and the demand. Our algorithm partitions the links into buckets. Every bucket consists of a set of links that have nearly equivalent reception powers. We denote the number of nonempty buckets by $\sigdiv$. Our algorithm obtains an approximation ratio of $O(\sigdiv \cdot \log n)$, where $n$ denotes the number of nodes. For the case of linear powers $\sigdiv =1$, hence the approximation ratio of the algorithm is $O(\log n)$. This is the first practical approximation algorithm for linear powers with an approximation ratio that depends only on $n$ (and not on the max-to-min distance ratio). If the transmission power of each link is part of the input (and arbitrary), then $\sigdiv = O(\logΓ+ \log Δ)$, where $Γ$ denotes the ratio of the max-to-min power, and $Δ$ denotes the ratio of the max-to-min distance. Hence, the approximation ratio is $O(\log n \cdot (\logΓ+ \log Δ))$. Finally, we consider the case that the algorithm needs to assign powers to each link in a range $[\pmin,\pmax]$. An extension of the algorithm to this case achieves an approximation ratio of $O[(\log n + \log \log Γ) \cdot (\logΓ+ \log Δ)]$.

cs.DS↗
arXiv2011

Real-Time Video Streaming in Multi-hop Wireless Static Ad Hoc Networks

We deal with the problem of streaming multiple video streams between pairs of nodes in a multi-hop wireless ad hoc network. The nodes are static, know their locations, and are synchronized (via GPS). We introduce a new interference model that uses variable interference radiuses. We present an algorithm for computing a frequency assignment and a schedule whose goal is to maximize throughput over all the video streams. In addition, we developed a localized flow-control mechanism to stabilize the queue lengths. We simulated traffic scheduled by the algorithm using OMNET++/MixiM (i.e., physical SINR interference model with 802.11g) to test whether the computed throughput is achieved. The results of the simulation show that the computed solution is \SINR-feasible and achieves predictable stable throughputs.

cs.NI↗