Demand-Aware Network Design with Minimal Congestion and … · 2019-05-05 · Challenges!6 Low...
Transcript of Demand-Aware Network Design with Minimal Congestion and … · 2019-05-05 · Challenges!6 Low...
Demand-Aware Network Design with Minimal Congestion
and Route Lengths
INFOCOM 2019
Chen Avin , Kaushik Mondal, Stefan Schmid
Motivation
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Motivation• Traditionally, networks topologies
designs are demand oblivious:
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Motivation• Traditionally, networks topologies
designs are demand oblivious:
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Motivation• Traditionally, networks topologies
designs are demand oblivious:• optimized for the “worst-case”:
all-to-all communications
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Motivation• Traditionally, networks topologies
designs are demand oblivious:• optimized for the “worst-case”:
all-to-all communications• e.g., Fat-tree topologies
provide (almost) a fullbisection bandwidth
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Motivation• Traditionally, networks topologies
designs are demand oblivious:• optimized for the “worst-case”:
all-to-all communications• e.g., Fat-tree topologies
provide (almost) a fullbisection bandwidth
• But…
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Motivation
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Motivation• Traffic is growing fast
!3Aggregate Server Traffic in Google datacenter
Jupiter rising @ SIGCOMM 2015
Motivation• Traffic is growing fast• Real communication patterns are sparse
and feature structure (?!)
!3Aggregate Server Traffic in Google datacenter
Jupiter rising @ SIGCOMM 2015Heatmap of rack-to-rack traffic ProjecToR @ SIGCOMM 2016
Motivation• Traffic is growing fast• Real communication patterns are sparse
and feature structure (?!)• Can be exploited if demand is known:
demand-aware design
!3Aggregate Server Traffic in Google datacenter
Jupiter rising @ SIGCOMM 2015Heatmap of rack-to-rack traffic ProjecToR @ SIGCOMM 2016
Demand-Aware Design?
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Application Layer
Transport Layer
Network Layer
Link / Physical Layer
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Demand-Aware Design?
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Application Layer
Transport Layer
Network Layer
Link / Physical Layer
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Demand-Aware Design?
!4
Application Layer
Transport Layer
Network Layer
Link / Physical Layer
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Demand-Aware Design?
!4
Application Layer
Transport Layer
Network Layer
Link / Physical Layer
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Demand-Aware Design?
!4
Application Layer
Transport Layer
Network Layer
Link / Physical Layer ?!
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Demand-Aware Design?
!4
Application Layer
Transport Layer
Network Layer
Link / Physical Layer ?!
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Demand-Aware Design?
!4
Application Layer
Transport Layer
Network Layer
Link / Physical Layer ?!Even in real time!
Networks Capable of Change.Jennifer Rexford.
Infocom 2019 Keynote.
Goal
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Goal• Design a demand aware, bounded
degree (scalable) networks with:
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Goal• Design a demand aware, bounded
degree (scalable) networks with:1. Short average route length (l),
and
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Goal• Design a demand aware, bounded
degree (scalable) networks with:1. Short average route length (l),
and 2. Low congestion (c):
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Goal• Design a demand aware, bounded
degree (scalable) networks with:1. Short average route length (l),
and 2. Low congestion (c):
• Both are importantmeasures of efficiency
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Challenges
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Challenges
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Short route length: bottleneck
Chen Avin, Kaushik Mondal and Stefan Schmid Demand-Aware Network Designs of Bounded Degree. DISC 2017
Challenges
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Low congestion: high degree/long routes
Short route length: bottleneck
Chen Avin, Kaushik Mondal and Stefan Schmid Demand-Aware Network Designs of Bounded Degree. DISC 2017
Challenges
!6
Low congestion: high degree/long routes
Demand-Aware Network Design withMinimal Congestion and Route Lengths
Chen AvinCommunication Systems Engineering Dept.Ben Gurion University of the Negev, Israel
Kaushik MondalCommunication Systems Engineering Dept.Ben Gurion University of the Negev, Israel
Stefan SchmidFaculty of Computer ScienceUniversity of Vienna, Austria
Abstract—Emerging communication technologies allow to re-
configure the physical network topology at runtime, enabling
demand-aware networks (DANs): networks whose topology is opti-
mized toward the workload they serve. However, today, only little
is known about the fundamental algorithmic problems underlying
the design of such demand-aware networks. This paper presents
the first bounded-degree, demand-aware network, cl-DAN, which
minimizes both congestion and route lengths. The designed
network is provably (asymptotically) optimal in each dimension
individually: we show that there do not exist any bounded-degree
networks providing shorter routes (independently of the load),
nor do there exist networks providing lower loads (independently
of the route lengths). The main building block of the designed
cl-DAN networks are ego-trees: communication sources arrange
their communication partners in an optimal tree, individually.
While the union of these ego-trees forms the basic structure of
cl-DANs, further techniques are presented to ensure bounded
degrees (for scalability).
I. INTRODUCTION
A. MotivationData center networks have become a critical infrastructure of
our digital society. With the trend toward more data-intensiveapplications, data center network traffic is growing quickly [7],[31]. As much of this traffic is internal to the data center (e.g.,traffic due to scatter-gather and batch computing applications),the design of efficient data center networks has received muchattention over the last years [23].
Traditionally, data center designs are demand-oblivious andstatic: they are optimized for the “worst-case”, e.g., they(almost) provide a full bisection bandwidth, allowing to servedense, all-to-all communication patterns. Empirical studieshowever show that real communication patterns are usually farfrom all-to-all. Rather, traffic patterns feature spatial localityand are sparse [5], [9], [13], [19], [21], [26]: only a smallfraction of all possible source-destination pairs are involved inintensive communications at any time.
The advent of novel optical technologies which allow toreconfigure the physical network topology [10], [15], [20], [21],heralds a paradigm shift: using these technologies, data centerdesigns can be reconfigured and optimized toward their demand,i.e., they become demand-aware. In particular, a demand-awarenetwork design may connect frequently communicating nodes“better”: the network provides shorter routes between suchnodes (lower latency, energy consumption etc.) and aims toreduce congestion by keeping traffic local (lower load, lessqueuing delays, etc.).
(a) (b) (c)Fig. 1. Challenge of designing demand-aware networks: (a) Optimizing forroute lengths only may result in bottlenecks and high loads. (b) Optimizing forcongestion only, by distributing load across multiple paths, can result in longroutes. (c) Ideally, we aim to design networks that minimize both congestionand route lengths, using a small number of links (constant degree).
However, only little is known today about the algorithmicchallenge of designing demand-aware networks which providelow congestion and short routes (in the number of hops), fora given communication pattern. This is the topic of our paper(see also Figure 1).
At first sight, it may seem that designing networks providingboth short routes and minimal load is hard and faces a tradeoff:to better balance loads, it may be necessary to route flows alonglonger paths. Yet, as we show in this paper, a solution can beefficiently computed which is almost optimal both in termsof route length and congestion, independently (i.e., withouttradeoff).
B. The Demand-Aware Network Design Problem
Intuitively, the demand-aware network design problem canbe stated as follows (a formal model will follow later). Weare given a set of n nodes (e.g., top-of-rack switches [21])interacting according to a certain communication pattern: afrequency distribution represented as matrix or (weighted)demand graph.
Our goal is to design a demand-aware network, cl-DAN,together with a routing scheme, which serves this communica-tion pattern providing low congestion and shorth route lengths.The designed network should be scalable, i.e., of boundeddegree (e.g., reconfigurable links may consume space and/or
Short route length: bottleneck
Chen Avin, Kaushik Mondal and Stefan Schmid Demand-Aware Network Designs of Bounded Degree. DISC 2017
Challenges: An Example
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Demand Distribution
Goal: design an optimal network with bounded degree 3
Challenges: An Example
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Demand Distribution Route length is minimum, not congestion
Goal: design an optimal network with bounded degree 3
Challenges: An Example
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Demand Distribution Route length is minimum, not congestion
Goal: design an optimal network with bounded degree 3
Challenges: An Example
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Demand Distribution Route length is minimum, not congestion
Congestion is minimum, not route length
Goal: design an optimal network with bounded degree 3
Challenges: An Example
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Demand Distribution Route length is minimum, not congestion
Congestion is minimum, not route length
Can we optimize both simultaneously?
Goal: design an optimal network with bounded degree 3
Model and Definitions
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Model and Definitions• Demand joint distribution
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Model and Definitions• Demand joint distribution• A network
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Model and Definitions• Demand joint distribution• A network• A routing scheme
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Model and Definitions• Demand joint distribution• A network• A routing scheme • The congestion:
!8
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Model and Definitions• Demand joint distribution• A network• A routing scheme • The congestion:
• The weighted path length
!8
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Goal: cl-DAN Design
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Goal: cl-DAN Design
!9
(↵,�)<latexit sha1_base64="jLKg44kMhMs2M1Xfd8/ZYyLpPoI=">AAAB+HicbVDLSgNBEOz1GeMjqx69DAYhgoRdFfQY8CJ4iWAekF1C72Q2GTL7YGZWiCFf4sWDIl79FG/+jZNkD5pY0FBUddPdFaSCK+0439bK6tr6xmZhq7i9s7tXsvcPmirJJGUNmohEtgNUTPCYNTTXgrVTyTAKBGsFw5up33pkUvEkftCjlPkR9mMecoraSF27VPFQpAM8I17ANJ527bJTdWYgy8TNSRly1Lv2l9dLaBaxWFOBSnVcJ9X+GKXmVLBJ0csUS5EOsc86hsYYMeWPZ4dPyIlReiRMpKlYk5n6e2KMkVKjKDCdEeqBWvSm4n9eJ9PhtT/mcZppFtP5ojATRCdkmgLpccmoFiNDkEpubiV0gBKpNlkVTQju4svLpHledS+q7v1luXaXx1GAIziGCrhwBTW4hTo0gEIGz/AKb9aT9WK9Wx/z1hUrnzmEP7A+fwBau5JE</latexit>
Input: matrix, degree
D,�<latexit sha1_base64="dhHBLegVOrV+0dzk94dPReYAq5I=">AAAB/HicbVDLSsNAFJ34rPUV7dLNYBFcSElU0GXBLgQ3FewDmlAm09t26GQSZiZCCPVX3LhQxK0f4s6/cdJmoa0HBg7n3Ms9c4KYM6Ud59taWV1b39gsbZW3d3b39u2Dw7aKEkmhRSMeyW5AFHAmoKWZ5tCNJZAw4NAJJje533kEqVgkHnQagx+SkWBDRok2Ut+ueCHRY0p41pieYa8BXJO+XXVqzgx4mbgFqaICzb795Q0imoQgNOVEqZ7rxNrPiNSMcpiWvURBTOiEjKBnqCAhKD+bhZ/iE6MM8DCS5gmNZ+rvjYyESqVhYCbzqGrRy8X/vF6ih9d+xkScaBB0fmiYcKwjnDeBB0wC1Tw1hFDJTFZMx0QSqk1fZVOCu/jlZdI+r7kXNff+slq/K+oooSN0jE6Ri65QHd2iJmohilL0jF7Rm/VkvVjv1sd8dMUqdiroD6zPHyk0lHk=</latexit>
Goal: cl-DAN Design
!9
(↵,�)<latexit sha1_base64="jLKg44kMhMs2M1Xfd8/ZYyLpPoI=">AAAB+HicbVDLSgNBEOz1GeMjqx69DAYhgoRdFfQY8CJ4iWAekF1C72Q2GTL7YGZWiCFf4sWDIl79FG/+jZNkD5pY0FBUddPdFaSCK+0439bK6tr6xmZhq7i9s7tXsvcPmirJJGUNmohEtgNUTPCYNTTXgrVTyTAKBGsFw5up33pkUvEkftCjlPkR9mMecoraSF27VPFQpAM8I17ANJ527bJTdWYgy8TNSRly1Lv2l9dLaBaxWFOBSnVcJ9X+GKXmVLBJ0csUS5EOsc86hsYYMeWPZ4dPyIlReiRMpKlYk5n6e2KMkVKjKDCdEeqBWvSm4n9eJ9PhtT/mcZppFtP5ojATRCdkmgLpccmoFiNDkEpubiV0gBKpNlkVTQju4svLpHledS+q7v1luXaXx1GAIziGCrhwBTW4hTo0gEIGz/AKb9aT9WK9Wx/z1hUrnzmEP7A+fwBau5JE</latexit>
Input: matrix, degree
D,�<latexit sha1_base64="dhHBLegVOrV+0dzk94dPReYAq5I=">AAAB/HicbVDLSsNAFJ34rPUV7dLNYBFcSElU0GXBLgQ3FewDmlAm09t26GQSZiZCCPVX3LhQxK0f4s6/cdJmoa0HBg7n3Ms9c4KYM6Ud59taWV1b39gsbZW3d3b39u2Dw7aKEkmhRSMeyW5AFHAmoKWZ5tCNJZAw4NAJJje533kEqVgkHnQagx+SkWBDRok2Ut+ueCHRY0p41pieYa8BXJO+XXVqzgx4mbgFqaICzb795Q0imoQgNOVEqZ7rxNrPiNSMcpiWvURBTOiEjKBnqCAhKD+bhZ/iE6MM8DCS5gmNZ+rvjYyESqVhYCbzqGrRy8X/vF6ih9d+xkScaBB0fmiYcKwjnDeBB0wC1Tw1hFDJTFZMx0QSqk1fZVOCu/jlZdI+r7kXNff+slq/K+oooSN0jE6Ri65QHd2iJmohilL0jF7Rm/VkvVjv1sd8dMUqdiroD6zPHyk0lHk=</latexit>
Output: cl-DAN
N 2 N�,�(N)<latexit sha1_base64="wLnTFDnBaqnp4QhRinGOdX/I5lY=">AAACDnicbVDLSgNBEJyNrxhfUY9eBkMggoRdFfQYUFAQQgTzgGwIvZNJMmRmdpmZFcKSL/Dir3jxoIhXz978GyePgyYWNBRV3XR3BRFn2rjut5NaWl5ZXUuvZzY2t7Z3srt7NR3GitAqCXmoGgFoypmkVcMMp41IURABp/VgcDn26w9UaRbKezOMaEtAT7IuI2Cs1M7my9hnEvsCTJ8AT8qjduJfUW5gdIz9axACCuWjdjbnFt0J8CLxZiSHZqi0s19+JySxoNIQDlo3PTcyrQSUYYTTUcaPNY2ADKBHm5ZKEFS3ksk7I5y3Sgd3Q2VLGjxRf08kILQeisB2js/W895Y/M9rxqZ70UqYjGJDJZku6sYcmxCPs8EdpigxfGgJEMXsrZj0QQExNsGMDcGbf3mR1E6K3mnRuzvLlW5ncaTRATpEBeShc1RCN6iCqoigR/SMXtGb8+S8OO/Ox7Q15cxm9tEfOJ8/jqabLQ==</latexit>
Goal: cl-DAN Design
!9
(↵,�)<latexit sha1_base64="jLKg44kMhMs2M1Xfd8/ZYyLpPoI=">AAAB+HicbVDLSgNBEOz1GeMjqx69DAYhgoRdFfQY8CJ4iWAekF1C72Q2GTL7YGZWiCFf4sWDIl79FG/+jZNkD5pY0FBUddPdFaSCK+0439bK6tr6xmZhq7i9s7tXsvcPmirJJGUNmohEtgNUTPCYNTTXgrVTyTAKBGsFw5up33pkUvEkftCjlPkR9mMecoraSF27VPFQpAM8I17ANJ527bJTdWYgy8TNSRly1Lv2l9dLaBaxWFOBSnVcJ9X+GKXmVLBJ0csUS5EOsc86hsYYMeWPZ4dPyIlReiRMpKlYk5n6e2KMkVKjKDCdEeqBWvSm4n9eJ9PhtT/mcZppFtP5ojATRCdkmgLpccmoFiNDkEpubiV0gBKpNlkVTQju4svLpHledS+q7v1luXaXx1GAIziGCrhwBTW4hTo0gEIGz/AKb9aT9WK9Wx/z1hUrnzmEP7A+fwBau5JE</latexit>
Input: matrix, degree
D,�<latexit sha1_base64="dhHBLegVOrV+0dzk94dPReYAq5I=">AAAB/HicbVDLSsNAFJ34rPUV7dLNYBFcSElU0GXBLgQ3FewDmlAm09t26GQSZiZCCPVX3LhQxK0f4s6/cdJmoa0HBg7n3Ms9c4KYM6Ud59taWV1b39gsbZW3d3b39u2Dw7aKEkmhRSMeyW5AFHAmoKWZ5tCNJZAw4NAJJje533kEqVgkHnQagx+SkWBDRok2Ut+ueCHRY0p41pieYa8BXJO+XXVqzgx4mbgFqaICzb795Q0imoQgNOVEqZ7rxNrPiNSMcpiWvURBTOiEjKBnqCAhKD+bhZ/iE6MM8DCS5gmNZ+rvjYyESqVhYCbzqGrRy8X/vF6ih9d+xkScaBB0fmiYcKwjnDeBB0wC1Tw1hFDJTFZMx0QSqk1fZVOCu/jlZdI+r7kXNff+slq/K+oooSN0jE6Ri65QHd2iJmohilL0jF7Rm/VkvVjv1sd8dMUqdiroD6zPHyk0lHk=</latexit>
Output: cl-DAN
N 2 N�,�(N)<latexit sha1_base64="wLnTFDnBaqnp4QhRinGOdX/I5lY=">AAACDnicbVDLSgNBEJyNrxhfUY9eBkMggoRdFfQYUFAQQgTzgGwIvZNJMmRmdpmZFcKSL/Dir3jxoIhXz978GyePgyYWNBRV3XR3BRFn2rjut5NaWl5ZXUuvZzY2t7Z3srt7NR3GitAqCXmoGgFoypmkVcMMp41IURABp/VgcDn26w9UaRbKezOMaEtAT7IuI2Cs1M7my9hnEvsCTJ8AT8qjduJfUW5gdIz9axACCuWjdjbnFt0J8CLxZiSHZqi0s19+JySxoNIQDlo3PTcyrQSUYYTTUcaPNY2ADKBHm5ZKEFS3ksk7I5y3Sgd3Q2VLGjxRf08kILQeisB2js/W895Y/M9rxqZ70UqYjGJDJZku6sYcmxCPs8EdpigxfGgJEMXsrZj0QQExNsGMDcGbf3mR1E6K3mnRuzvLlW5ncaTRATpEBeShc1RCN6iCqoigR/SMXtGb8+S8OO/Ox7Q15cxm9tEfOJ8/jqabLQ==</latexit>
Where
Optimal congestion
Goal: cl-DAN Design
!9
(↵,�)<latexit sha1_base64="jLKg44kMhMs2M1Xfd8/ZYyLpPoI=">AAAB+HicbVDLSgNBEOz1GeMjqx69DAYhgoRdFfQY8CJ4iWAekF1C72Q2GTL7YGZWiCFf4sWDIl79FG/+jZNkD5pY0FBUddPdFaSCK+0439bK6tr6xmZhq7i9s7tXsvcPmirJJGUNmohEtgNUTPCYNTTXgrVTyTAKBGsFw5up33pkUvEkftCjlPkR9mMecoraSF27VPFQpAM8I17ANJ527bJTdWYgy8TNSRly1Lv2l9dLaBaxWFOBSnVcJ9X+GKXmVLBJ0csUS5EOsc86hsYYMeWPZ4dPyIlReiRMpKlYk5n6e2KMkVKjKDCdEeqBWvSm4n9eJ9PhtT/mcZppFtP5ojATRCdkmgLpccmoFiNDkEpubiV0gBKpNlkVTQju4svLpHledS+q7v1luXaXx1GAIziGCrhwBTW4hTo0gEIGz/AKb9aT9WK9Wx/z1hUrnzmEP7A+fwBau5JE</latexit>
Input: matrix, degree
D,�<latexit sha1_base64="dhHBLegVOrV+0dzk94dPReYAq5I=">AAAB/HicbVDLSsNAFJ34rPUV7dLNYBFcSElU0GXBLgQ3FewDmlAm09t26GQSZiZCCPVX3LhQxK0f4s6/cdJmoa0HBg7n3Ms9c4KYM6Ud59taWV1b39gsbZW3d3b39u2Dw7aKEkmhRSMeyW5AFHAmoKWZ5tCNJZAw4NAJJje533kEqVgkHnQagx+SkWBDRok2Ut+ueCHRY0p41pieYa8BXJO+XXVqzgx4mbgFqaICzb795Q0imoQgNOVEqZ7rxNrPiNSMcpiWvURBTOiEjKBnqCAhKD+bhZ/iE6MM8DCS5gmNZ+rvjYyESqVhYCbzqGrRy8X/vF6ih9d+xkScaBB0fmiYcKwjnDeBB0wC1Tw1hFDJTFZMx0QSqk1fZVOCu/jlZdI+r7kXNff+slq/K+oooSN0jE6Ri65QHd2iJmohilL0jF7Rm/VkvVjv1sd8dMUqdiroD6zPHyk0lHk=</latexit>
Output: cl-DAN
N 2 N�,�(N)<latexit sha1_base64="wLnTFDnBaqnp4QhRinGOdX/I5lY=">AAACDnicbVDLSgNBEJyNrxhfUY9eBkMggoRdFfQYUFAQQgTzgGwIvZNJMmRmdpmZFcKSL/Dir3jxoIhXz978GyePgyYWNBRV3XR3BRFn2rjut5NaWl5ZXUuvZzY2t7Z3srt7NR3GitAqCXmoGgFoypmkVcMMp41IURABp/VgcDn26w9UaRbKezOMaEtAT7IuI2Cs1M7my9hnEvsCTJ8AT8qjduJfUW5gdIz9axACCuWjdjbnFt0J8CLxZiSHZqi0s19+JySxoNIQDlo3PTcyrQSUYYTTUcaPNY2ADKBHm5ZKEFS3ksk7I5y3Sgd3Q2VLGjxRf08kILQeisB2js/W895Y/M9rxqZ70UqYjGJDJZku6sYcmxCPs8EdpigxfGgJEMXsrZj0QQExNsGMDcGbf3mR1E6K3mnRuzvLlW5ncaTRATpEBeShc1RCN6iCqoigR/SMXtGb8+S8OO/Ox7Q15cxm9tEfOJ8/jqabLQ==</latexit>
Where
Optimal congestion
&Optimal path length
!10
A Building Block: EgoTree
!10
• A single source multiple destination problem
A Building Block: EgoTree
!10
• A single source multiple destination problem
A Building Block: EgoTree
S
p̄ = {p1, p2, …, pk}
!10
…Δ
• A single source multiple destination problem
•
A Building Block: EgoTree
EgoTree(s, p̄, Δ) S
p̄ = {p1, p2, …, pk}
Binary Trees
!10
…Δ
• A single source multiple destination problem
•
• Optimizes both C and L
A Building Block: EgoTree
EgoTree(s, p̄, Δ) S
p̄ = {p1, p2, …, pk}
Binary Trees
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: A Greedy Construction
• Sort = {p1, p2, …, pk} from large to small• Greedily Place destination nodes (one at a
time)
!11
…
S
T1 T2 … TΔ
EgoTree: An Example• Ego-tree is not balanced w.r.t. sizes of
the subtrees• Almost balanced w.r.t. the probability
mass that defines congestion
!12
EgoTree: An Example• Ego-tree is not balanced w.r.t. sizes of
the subtrees• Almost balanced w.r.t. the probability
mass that defines congestion
!12
Analysis on Congestion
!13
Analysis on Congestion• Minimizing congestion is a NP-Hard problem
• provides 4/3 approximation to the minimum congestion (i.e., Longest Processing Time [Graham69])
!13
EgoTree(s, p̄, Δ)
Analysis on Route-Length
!14
Analysis on Route-Length• Considering all the binary subtrees and
using entropy grouping properties, we have an Entropy bound:
!14
Analysis on Route-Length• On any optimal Δ-ary tree:
• Combining all, we now have optimality on L
!15
H(p̄)log2(Δ + 1)
≤ L(p̄, T*Δ) ≤ L(p̄, T*s ) ≤ H(p̄)
Analysis on Route-Length• On any optimal Δ-ary tree:
• Combining all, we now have optimality on L
!15
H(p̄)log2(Δ + 1)
≤ L(p̄, T*Δ) ≤ L(p̄, T*s ) ≤ H(p̄)
!16
From Trees to Networks
!16
From Trees to Networks
!17
From Trees to Networks
• Real distributions are sparse: datacentre's traffic shows demand distributions are sparse
!17
From Trees to Networks
• Real distributions are sparse: datacentre's traffic shows demand distributions are sparse
• We assume a distribution D with average degree ⍴
!17
From Trees to Networks
• Real distributions are sparse: datacentre's traffic shows demand distributions are sparse
• We assume a distribution D with average degree ⍴
!17
From Trees to Networks
• Real distributions are sparse: datacentre's traffic shows demand distributions are sparse
• We assume a distribution D with average degree ⍴
• ⍴ is a constant
!17
From Trees to Networks
• Real distributions are sparse: datacentre's traffic shows demand distributions are sparse
• We assume a distribution D with average degree ⍴
• ⍴ is a constant
• Half of the nodes of lowest degree are defined as low degree nodes; others are high degree nodes
!17
From Trees to Networks
Sparse Distributions• Proof idea i
!18
Sparse Distributions• Proof idea i i
Optimal bounded degree tree
!18
Sparse Distributions• Proof idea i
i j
i
Optimal bounded degree treeProblem
!18
Sparse Distributions• Proof idea i
i j
i
Optimal bounded degree treeProblem
Solution - “helper” nodes!18
Sparse Distributions• Proof idea i
i j i j
i
Optimal bounded degree treeProblem
Solution - “helper” nodes!18
Ego-tree Modification • Modify ego-tree Tu of a high degree node u
to T’u
• let v be a high degree neighbor of u: b be the helper node• we remove v from ego-tree of u if p(u,b)>p(u,v) • else we put b in place of v
!19
cl-DANs : Sparse Distributions
!20
cl-DANs : Sparse Distributions
• For Δ=12 ⍴
!20
cl-DANs : Sparse Distributions
• For Δ=12 ⍴• Degree of nodes are at most Δ
!20
cl-DANs : Sparse Distributions
• For Δ=12 ⍴• Degree of nodes are at most Δ• Congestion is at most:
!20
C(D,�(N)) 1 + 8/9�C⇤(D,�)<latexit sha1_base64="mbbXKXL7pcKOIymk13piKOMv1tA=">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</latexit>
cl-DANs : Sparse Distributions
• For Δ=12 ⍴• Degree of nodes are at most Δ• Congestion is at most:
!20
C(D,�(N)) 1 + 8/9�C⇤(D,�)<latexit sha1_base64="mbbXKXL7pcKOIymk13piKOMv1tA=">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</latexit>
cl-DANs : Sparse Distributions
• For Δ=12 ⍴• Degree of nodes are at most Δ• Congestion is at most:
• Average Path length is at most
!20
C(D,�(N)) 1 + 8/9�C⇤(D,�)<latexit sha1_base64="mbbXKXL7pcKOIymk13piKOMv1tA=">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</latexit>
cl-DANs : Sparse Distributions
• For Δ=12 ⍴• Degree of nodes are at most Δ• Congestion is at most:
• Average Path length is at most
!20
C(D,�(N)) 1 + 8/9�C⇤(D,�)<latexit sha1_base64="mbbXKXL7pcKOIymk13piKOMv1tA=">AAACLXicbVDLSgMxFM34tr6qLt0Ei9Cq1BkV1F2hBQVBFKwKnVrupLc1mMwMSUYoQ3/Ijb8igouKuPU3TB8LXwcCh3POJfeeIBZcG9ftOWPjE5NT0zOzmbn5hcWl7PLKlY4SxbDKIhGpmwA0Ch5i1XAj8CZWCDIQeB3cl/v+9QMqzaPw0nRirEtoh7zFGRgrNbKVct6XYO4YiLTS3ab+MUgJ+bNCgfoCqUe36OHOEfUrKAzQ8u3mj/hQLjSyObfoDkD/Em9EcmSE80b2xW9GLJEYGiZA65rnxqaegjKcCexm/ERjDOwe2lizNASJup4Oru3SDas0aStS9oWGDtTvEylIrTsysMn+qvq31xf/82qJaR3WUx7GicGQDT9qJYKaiParo02ukBnRsQSY4nZXyu5AATO24Iwtwft98l9ytVv09orexX6udDqqY4askXWSJx45ICVyQs5JlTDySJ5Jj7w5T86r8+58DKNjzmhmlfyA8/kFlQqkvg==</latexit>
cl-DANs : Sparse Distributions
• What have we shown?• For sparse distributions we can have
!21
cl-DANs : Sparse Distributions
• What have we shown?• For sparse distributions we can have
!21
Near optimal congestion
Near optimal path length
cl-DANs : Sparse Distributions
• What have we shown?• For sparse distributions we can have
!21
Near optimal congestion
Near optimal path length
Take home
!22
Take home•Demand Aware Networks are possible
!22
Take home•Demand Aware Networks are possible
•The “challenge” is Self-Adjusting Networks
•without knowing the future
!22
Take home•Demand Aware Networks are possible
•The “challenge” is Self-Adjusting Networks
•without knowing the future
•What about:
• Δ is forced.
• routing protocols?
•cost metrics?
•Sync with upper layers
!22
Take home•Demand Aware Networks are possible
•The “challenge” is Self-Adjusting Networks
•without knowing the future
•What about:
• Δ is forced.
• routing protocols?
•cost metrics?
•Sync with upper layers
•Much work and Interesting…
!22
Thank you!Toward Demand-Aware Networking: A Theory for Self-Adjusting NetworksChen Avin and Stefan Schmid.SIGCOMM CCR, October 2018.Demand-Aware Network Designs of Bounded DegreeChen Avin, Kaushik Mondal, and Stefan Schmid.31st International Symposium on Distributed Computing (DISC), Vienna, Austria, October 2017.
Online Balanced RepartitioningChen Avin, Andreas Loukas, Maciej Pacut, and Stefan Schmid.30th International Symposium on Distributed Computing (DISC), Paris, France, September 2016.
rDAN: Toward Robust Demand-Aware Network DesignsChen Avin, Alexandr Hercules, Andreas Loukas, and Stefan Schmid.Information Processing Letters (IPL), Elsevier, 2018.SplayNet: Towards Locally Self-Adjusting NetworksStefan Schmid, Chen Avin, Christian Scheideler, Michael Borokhovich, Bernhard Haeupler, and Zvi Lotker.IEEE/ACM Transactions on Networking (TON), Volume 24, Issue 3, 2016. Early version: IEEE IPDPS 2013.
Demand-aware network design with minimal congestion and route lengthsC. Avin, K. Mondal, and S. Schmid, IEEE INFOCOM, 2019.Distributed self-adjusting tree networksB. Peres, O. Souza, O. Goussevskaia, S. Schmid, and C. Avin,Proc. IEEE INFOCOM, 2019.
Furth
er R
eadi
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