Research

Interests

Methods

    Networks
    Resource Allocation
    Combinatorial Optimization
    Mathematical Programming
    Design and Analysis of Algorithms
    (Mixed-)Integer and Linear Programming
    Approximation Algorithms
    Computational Complexity
    Structural Graph Theory
    Verification: Theorem Provers and Modelchecking

The Virtual Network Embedding Problem (2015-2019)

The Virtual Network Embedding Problem (VNEP) captures the essence of resource allocation problems in virtualized networks: users specify their computation and communication demands via virtual networks, which are then embedded on the physical network (ISP or data center networks).
While the VNEP has been extensively studied for more than 15 years and several hundred papers have been published on the challenges associated to it, only few theoretic results were obtained . Together with Stefan Schmid, I derived the first parametrized approximation algorithms for the VNEP together with a comprehensive list of NP-hardness and inapproximability results. Besides the theoretic results, my team of student workers and I implemented all algorithms and evaluated them in a large scale evaluation.

Figure: Exemplary embedding of a virtual network together with the demands of the virtual network and the used/available capacity of the physical network.

publications GitHub project

Middlebox Placement (2015-2018)

Today's networks contain specific (potentially virtualized) hardware appliances called middleboxes to perform network functions, as, e.g., firewalls, network-address translators, etc. Whenever a flow is to be routed through such an appliance, a specific middlebox together with routes to and from it have to be chosen.
Together with Tamás Lukvoszki and Stefan Schmid, I developed approximations to place middleboxes to connect the maximum number of flows. Based on a greedy scheme, the approximation can be used to incrementally place middleboxes, while not losing the theoretic performance guarantee.
Figure: Results of various experiments with respect to the achieved approximation guarantee and the runtime of the greedy approximations compared to the exact Integer Program.
publications GitHub project

Optimal Scheduling of Tutors (2014-2017)

As part of my teaching duties, I had to schedule and assign several dozens of tutors to various different tasks and rooms for a 2-week block course for 600-1000 students. With around 25-40 tutors, around 600 hours of planned activities and even more booked rooms, I decided to develop an optimization framework to conquer the complexity. Among the considered constraints and objectives are the following:
minimal deviation from teaching plan       optimized working hours according to preferences       fairness of work assignments       minimal number of room switches for tutors       optimized usage of tutorial room capacities       minimized number of assignment changes when re-planning

The tutor-planner was overall very successful and the tutors were especially satisfied, given that their preferences were met to an high degree (see plot on the left below).

Figure: Plan for a single day indicating tutorials and pc pool sessions.
Figure: Optimized relative working hours and happiness of tutors.

GitHub project

Scheduling Network Updates (2014-2017)

Virtualized networks allow to easily exert control of forwarding paths on the data plane. However, updating end-to-end routes in such Software-Defined Networks have to be scheduled correctly to not bypass critical middleboxes and to not introduce transient loops.
Headed by Stefan Schmid and Arne Ludwig, theoretical hardness proofs for this novel network update problem were obtained, while I was mainly responsible for developing exact algorithms for scheduling updates or deciding that updates are not possible without further overheard. Using large-scale evaluations, we showed that updates can often be performed without overhead while respecting both loop-freedom and middlebox traversal.

Figure: Visualization of the construction used to prove the NP-hardness of the Network Update Problem.

publications GitHub project

Stitching Paths at IXPs (2014-2016)

The Internet spans the entire world and most of the ISPs connect at Internet Exchange Points (IXPs). To facilitate novel applications as, e.g., tele-surgery, end-to-end paths supporting Quality-of-Service (QoS) guarantees need to be constructed between end points. To this end, a team around Vasileios Kotronis proposed the idea of Control Exchange Points (CXPs) to stitch paths of individual ISPs at IXPs while ensuring that the sub-paths of each ISP agree with the QoS-specification.
Within this project, I developed new heuristics and used linear programming to obtain baseline solutions. Our results indicated that using our efficient heuristics near-optimal solutions can be obtained, rendering the CXP approach practically feasible.
Figure: Overview of CXP approach: end-to-end paths are stitched at IXPs.
publications

UNIFY Project (2014-2016)

I was part of the EU FP7 Integrated Project UNIFY, which aimed at developing ways to innovate the core of ISP networks by virtualizing it:
Today, rigid network control limits the flexibility of service creation. We pursue full network and service virtualization to enable rich and flexible services and operational efficiency. The UNIFY consortium researches, develops and evaluates means to orchestrate, verify and observe end-to-end service delivery from home and enterprise networks through aggregation and core networks to data centres.
Figure: Overview of provisioning process for service chains.

Within the project, I contributed original theoretic research and worked on the architecture and the design of the central orchestration framework , which decides how to embed virtualized service chains inside the ISP networks.

publications UNIFY project homepage

Optimal Virtualized In-Network Processing (2013-2014)

In-network processing allows for the resource efficient deployment of communication tasks as e.g. multicast. Due to the ongoing effort to fully virtualize networks, several new optimization opportunities arose. Together with Stefan Schmid, I have initiated the study of where to place processing functionality and how to route data in a joint fashion, such that bandwidth can be traded off with node resources. We have coined this problem the Constrained Virtual Steiner Arborescence Problem (CVSAP) and devised a novel single-commodity flow integer formulation for CVSAP that can be solved efficiently using branch-and-cut. While even realistically sized instances can be solved near optimally within one hour, the formulation also enables a range of polynomial-time heuristics which find high-quality solutions with high efficacy in minutes.
Figure: isualization of an optimal world-wide aggregation tree.
publications project homepage

Temporal Virtual Network Embedding Problem (2012-2014)

The Temporal Virtual Network Embedding Problem (TVNEP) extends the classical Virtual Network Embedding Problem (VNEP) by introducing a temporal dimension: for each virtual network request a duration and a time interval is given in which it must be embedded. The TVNEP asks for finding suitable resources to embed the requests together with a feasible schedule, i.e. to find start and end times of the requests such that resource allocations are feasible at any point in time.

Figure: Visualization of our continuous-time event point model.

We have developed multiple Mixed Integer Programming formulations to obtain (near-)optimal solutions to this problem. For facilitating such exact methods, we have developed different state-space as well as symmetry reductions.

publications project homepage

Publications

Virtual Network Embedding Problem
Network Updates
Virtualized In-Network Processing
Service Chaining & Network Functions Virtualization
Resource Allocation in Specific Networks (non of the above)
Miscellaneous
Clear Selection

Conference Publications

    Modeling Adaptive Video Streaming Using Discrete-Time Analysis
Susanna Schwarzmann, Paula Breitbach, Thomas Zinner, Matthias Rost
International Teletraffic Congress (ITC), Budapest, Hungary, August 2019 (to appear)
   
    A Constant Approximation for Maximum Throughput Multicommodity Routing: And Its Application to Delay-Tolerant Network Scheduling
Mengxue Liu, Andrea W. Richa, Matthias Rost, Stefan Schmid
IEEE INFOCOM 2019, Paris, France, May 2019
IEEExplore        
   
    Charting the Complexity Landscape of Virtual Network Embeddings (★ Best Paper Award)
Matthias Rost, Stefan Schmid
IFIP Networking 2018, Zurich, Switzerland, May 2018
paper (pdf)         extended technical report (pdf)         slides (pdf)         bibtex
   
    Virtual Network Embedding Approximations: Leveraging Randomized Rounding
Matthias Rost, Stefan Schmid
IFIP Networking 2018, Zurich, Switzerland, May 2018
paper (pdf)         extended technical report (pdf)         slides (pdf)         bibtex
   
    An Approximation Algorithm for Path Computation and Function Placement in SDNs
Guy Even, Matthias Rost, Stefan Schmid
23rd International Colloquium on Structural Information and Communication Complexity (SIROCCO) 2016, Helsinki, Finland, July 2016
pre-proceedings (pdf)         slides (pdf)         bibtex
   
    Transiently Secure Network Updates
Arne Ludwig, Szymon Dudycz, Matthias Rost, Stefan Schmid
ACM SIGMETRICS 2016, Antibes Juan-Les-Pins, France, June 2016
ACM download         slides (pdf)         bibtex
   
    Stitching Inter-Domain Paths over IXPs
Vasileios Kotronis, Rowan Klöti, Matthias Rost, Panagiotis Georgopoulos, Bernhard Ager, Stefan Schmid, Xenofontas Dimitropoulos
ACM SIGCOMM SOSR 2016, Santa Clara, California, USA, March 2016
slides (pdf)         bibtex
   
    Investigating the Potential of the Inter-IXP Multigraph for the Provisioning of Guaranteed End-to-End Services
Vasileios Kotronis, Rowan Klöti, Matthias Rost, Panagiotis Georgopoulos, Bernhard Ager, Stefan Schmid, Xenofontas Dimitropoulos
SIGMETRICS 2015 (poster), Portland, Oregon, USA, June 2015
ACM download         bibtex
   
    It's About Time: On Optimal Virtual Network Embeddings under Temporal Flexibilities
Matthias Rost, Stefan Schmid and Anja Feldmann
28th IEEE International Parallel and Distributed Processing Symposium (IPDPS), Phoenix, Arizona, USA, May 2014
IEEE Xplore         slides (pdf)         bibtex
   
    VirtuCast: Multicast and Aggregation with In-Network Processing
  Matthias Rost, Stefan Schmid
  17th International Conference On Principles Of DIstributed Systems (OPODIS) 2013, Nice, France, December 2013
  springer link         slides (pdf)         project homepage         bibtex

Journal Publications

    Parametrized Complexity of Virtual Network Embeddings: Dynamic & Linear Programming Approximations
Matthias Rost, Elias Döhne, Stefan Schmid
ACM SIGCOMMM Computer Communication Review (CCR), 49.1, January 2019.
  paper (pdf)         ACM Digital Library         bibtex
   
    Approximate and incremental network function placement
Tamás Lukovszki, Matthias Rost, Stefan Schmid
Journal of Parallel and Distributed Computing 120, 2018.
  ScienceDirect
   
    Transiently policy-compliant network updates
Arne Ludwig, Szymon Dudycz, Matthias Rost, Stefan Schmid
IEEE/ACM Transactions on Networking, 26.6, September 2018
IEEExplore        
   
    It's a Match!: Near-Optimal and Incremental Middlebox Deployment
Tamás Lukovszki, Matthias Rost, Stefan Schmid
ACM SIGCOMMM Computer Communication Review (CCR), 46.1, January 2016.
  ACM Digital Library         bibtex
   
    Network service chaining with optimized network function embedding supporting service decompositions
Sahel Sahhaf, Wouter Tavernier, Matthias Rost, Stefan Schmid, Didier Colle, Mario Pickavet, Piet Demeester
Computer Networks, Elsevier
  ScienceDirect         bibtex
   
    Beyond the Stars: Revisiting Virtual Cluster Embeddings
Matthias Rost, Carlo Fürst and Stefan Schmid
ACM SIGCOMMM Computer Communication Review (CCR), 45.3, July 2015.
  ACM download         bibtex         talk at Télécom-ParisTech, September 2015 (pdf)

Workshop Publications

    Fast and Efficient Network Service Embedding Method with Adaptive Offloading to the Edge
  Balázs Németh, Márk Szalay, János Dóka, Matthias Rost, Stefan Schmid, Laszlo Toka, Balázs Sonkoly
  The 2nd Workshop on Integrating Edge Computing, Caching, and Offloading in Next Generation Networks (IECCO), INFOCOM 2018, Honolulu, HI, USA, April 2018.
   
    Efficient service graph embedding: A practical approach
  Balázs Németh, Balázs Sonkoly, Matthias Rost and Stefan Schmid.
  Second IEEE Workshop on Orchestration for Software Defined Infrastructures (O4SDI), NFV-SDN 2016, Palo Alto, CA, USA, November 2016.
  IEEE Xplore         bibtex
   
    Good Network Updates for Bad Packets: Waypoint Enforcement Beyond Destination-Based Routing Policies
  Arne Ludwig, Matthias Rost, Damien Foucard, and Stefan Schmid.
  13th ACM Workshop on Hot Topics in Networks (HotNets), Los Angeles, CA, USA, November 2014
  ACM download         bibtex
   
    Unifying the Programmability of Cloud and Carrier Infrastructure
  Pontus Skoldstrom, Balazs Sonkoly, Mario Kind, Fritz-Joachim Westphal, Wolfgang John, Jokin Garay, Eduardo Jacob, Janos Elek, David Jocha, Robert Szabo, Wouter Tavernier, George Agapiou, Antonio Manzalini, Matthias Rost, Nadi Sarrar, and Stefan Schmid.
  European Workshop on Software Defined Networking (EWSDN), Budapest, Hungary, September 2014

Technical Reports

    (FPT-)Approximation Algorithms for the Virtual Network Embedding Problem
  Matthias Rost and Stefan Schmid.
  arXiv:1803.04452 [cs.NI], March 2018
   
    Virtual Network Embedding Approximations: Leveraging Randomized Rounding
  Matthias Rost and Stefan Schmid.
  arXiv:1803.03622 [cs.NI], March 2018
   
    NP-Completeness and Inapproximability of the Virtual Network Embedding Problem and Its Variants
  Matthias Rost and Stefan Schmid.
  arXiv:1801.03162 [cs.NI], January 2018
   
    Approximate and Incremental Network Function Placement
  Tamas Lukovszki, Matthias Rost and Stefan Schmid.
  arXiv:1706.06496 [cs.NI], June 2017         bibtex
   
    Service Chain and Virtual Network Embeddings: Approximations using Randomized Rounding
  Matthias Rost and Stefan Schmid
  arxiv:1604.02180 [cs.NI], April 2016         bibtex
   
    An Approximation Algorithm for Path Computation and Function Placement in SDNs
  Guy Even, Matthias Rost and Stefan Schmid
  arxiv:1603.09158 [cs.NI], March 2016         bibtex
   
    KuVS Prize for the Best Master Thesis 2014: `Optimal Virtualized In-Network Processing with Applications to Aggregation and Multicast'
  Matthias Rost, Stefan Schmid, Andreas Bley and Anja Feldmann
  2015 International Conference on Networked Systems (NetSys), Cottbus, Germany, March 2015
  Summary of my Master Thesis (made available on the USB Proceedings of NetSys 2015)         bibtex         slides (pdf)         NetSys homepage
   
    Investigating the Potential of the Inter-IXP Multigraph for the Provisioning of Guaranteed End-to-End Services
  Vasileios Kotronis, Rowan Klöti, Matthias Rost, Panagiotis Georgopoulos, Bernhard Ager, Stefan Schmid, Xenofontas Dimitropoulos
  ETH Zurich, Laboratory TIK, February 2015.
  pdf         bibtex
   
    The Constrained Virtual Steiner Arborescence Problem: Formal Definition, Single-Commodity Integer Programming Formulation and Computational Evaluation
  Matthias Rost, Stefan Schmid
  arXiv:1310.0346 [cs.NI], October 2013         bibtex

Talks at Conferences (Invited or Contributed)

    Approximating the Virtual Network Embedding Problem: Theory and Practice
  Matthias Rost, Stefan Schmid
  23rd International Symposium on Mathematical Programming, Bordeaux, France, July 2018
  slides (pdf)
   
    Approximate Graph Embeddings in the Cloud
  Matthias Rost, Stefan Schmid
  3rd Highlights of Algorithms Conference, Amsterdam, Netherlands, June 2018
  poster (pdf)         slides (pdf)
   
    A Compact MIP for Aggregation and Multicast Trees under Flexible Routing and Function Placement
  Matthias Rost, Stefan Schmid
  22nd International Symposium on Mathematical Programming (ISMP), Pittsburgh, Pennsylvania, USA, July 2015
  Cluster: Combinatorial Optimization, Session: Routing and Facility Location
  slides (pdf)         Session Information
   
    KuVS Prize for the Best Master Thesis 2014: `Optimal Virtualized In-Network Processing with Applications to Aggregation and Multicast'
  Matthias Rost, Stefan Schmid, Andreas Bley and Anja Feldmann
  2015 International Conference on Networked Systems (NetSys), Cottbus, Germany, March 2015
  Summary of my Master Thesis (made available on the USB Proceedings of NetSys 2015)         bibtex         slides (pdf)         NetSys homepage

Ph.D. Thesis

    Virtual Network Embeddings: Theoretical Foundations and Provably Good Algorithms
Comittee: Rolf Niedermeier (head), Thomas Zinner, Stefan Schmid, Anja Feldmann, Harald Räcke
Technische Universität Berlin
Defense: March 25, 2019; Expected publication: September 2019
  Defense Slides

Master Thesis

    Optimal Virtualized In-Network Processing with Applications to Aggregation and Multicast
Advisors: Stefan Schmid, Andreas Bley, Anja Feldmann
Technische Universität Berlin, January 2014
★ Awarded with the Best Master Thesis Prize 2014 by the   Communication and Distributed Systems Group Special Interest Group (KuVS)
pdf         slides (pdf)         data & solver (tar.gz, 493MB, 3,7 GB unpacked)         bibtex         TU Berlin News (German)

Unpublished

    The Informal Guide to the Virtual Network Embedding MIP Creator (VNetEMC)
pdf         (source of the VNetEMC can be made available)

Other Talks (Conference talks see above)

    Hosted by Stefan Schmid, Aalborg University, August 2017
Beyond the Stars: Revisiting Virtual Cluster Embeddings
slides (pdf)
 
    FG INET Retreat, September 2016
Integer Linear Programming Primer
slides (pdf)         example data (tar.gz, 2.3 KB)
 
    Hosted by Tamaś Lukvoszki, Eötvös Loránd University, Budapest, February 2016
Beyond the Stars: Revisiting Virtual Cluster Embeddings
slides (pdf)
 
    Hosted by Petr Kuznetsov, Télécom ParisTech, September 2015
Beyond the Stars: Revisiting Virtual Cluster Embeddings
slides (pdf)
 
    NetAlgs seminar (hosted by Guy Even, organized by Boaz Patt-Shamir), Tel Aviv University, March 2015
VirtuCast
slides (pdf)
 
    Lehrstuhl für Kommunikationsnetze (hosted by Wolfgang Kellerer), TU München, August 2014
VirtuCast / Temporal Virtual Network Embedding Problem
slides (pdf)
 
    International Computer Science Institute (hosted by Robin Sommer), UC Berkeley, May 2014
VirtuCast / Temporal Virtual Network Embedding Problem
slides (pdf)
 
    Arizona State University (hosted by Andrea Richa), May 2014
VirtuCast / Temporal Virtual Network Embedding Problem
slides (pdf)
 
    ViNO project meeting (hosted by Stefan Schmid), TU Berlin, February 2014
VNetEMC / VirtuCast / Temporal Virtual Network Embedding Problem
slides (pdf)
 
    BigFoot project meeting , EURECOM (hosted by Pietro Michiardi), December 2013
VirtuCast
slides (pdf)

Bio

Full CV (pdf)

Work

since 04/2019 Postodoctoral researcher at Internet Measurement and Analysis Group, Technische Universität Berlin
01/2014 - 03/2019 Research and Teaching Assistant at Internet Network Architecture Group , Technische Universität Berlin
11/2011 - 12/2013 Student Research Assistant at Internet Network Architecture Group , Technische Universität Berlin
04/2009 - 09/2011 Tutor at the computer science department of Freie Universität Berlin
08/2007 - 02/2009 Student Software Developer at IVU Traffic Technologies AG (C/C++, PL/SQL)

Teaching (Research Assistant)

10/2018 - 03/2019 Internet Routing Seminar at Technische Universität Berlin
04/2018 - 09/2018 Internet Measurement Seminar at Technische Universität Berlin
10/2017 - 03/2018 (partly) Introduction to Programming (Einführung in die Prorgammierung) at Technische Universität Berlin
10/2016 - 03/2017 Introduction to Programming (Einführung in die Prorgammierung) at Technische Universität Berlin
10/2015 - 03/2016 Introduction to Programming (Einführung in die Prorgammierung) at Technische Universität Berlin
10/2014 - 03/2015 Introduction to Programming (Einführung in die Prorgammierung) at Technische Universität Berlin
04/2014 - 09/2014 Internet Measurement Seminar at Technische Universität Berlin

Teaching (Tutor)

9/2011 Computer Architecture (for pupils) at Freie Universität Berlin Berlin
9/2010 Computer Architecture (for pupils) at Freie Universität Berlin Berlin
04/2010 - 09/2010 Non-sequential Programming at Freie Universität Berlin Berlin
10/2009 - 03/2010 Operating Systems and Computer Networks at Freie Universität Berlin Berlin
04/2009 - 09/2009 Computer Architecture at Freie Universität Berlin Berlin

Education

04/2010 - 01/2014 Computer Science (M.Sc.) at Technische Universität Berlin
Thesis: 'Optimal Virtualized In-Network Processing with Applications to Aggregation and Multicast'
10/2010 - 09/2013 Mathematics (B.Sc.) at Freie Universität Berlin
10/2009 - 09/2010 Computer Science (M.Sc.) at Freie Universität Berlin
10/2006 - 09/2009 Computer Science (B.Sc.) at Freie Universität Berlin
Thesis: 'Modellierung und Lösung von Evakuierungsproblemen mittels Netzwerkflüssen'
             ('Modeling and Solving Evacuation Problems using Network Flows')

Awards & Grants

May 2018 Best Paper Award at IFIP Networking 2018 for the paper "Charting the Complexity of Virtual Network Embeddings" by Stefan Schmid and me
September 2017 Hackathon Winner at the   Gurobi-TomTom Mobility Maximization Challenge
March 2016 BMBF grant as part of the   Software Campus Program
March 2015 Best Master Thesis Prize 2014 by the   Communication and Distributed Systems Special Interest Group (KuVS) (a part of the   German Informatics Society and the   Information Technology Society)
10/2010-3/2013 Scholarship from the German National Academic Foundation (Studienstiftung des deutschen Volkes)
June 2006 DPG-Buchpreis 2006 from the German Physical Society (Deutsche Physikalische Gesellschaft) in recognition for outstanding achievements in physics

Contact

Address TU Berlin
Matthias Rost
MAR 4-4 / Room 4.031
Marchstr. 23
10587 Berlin
 
Office Hours by appointment
 
E-Mail mrost -at- inet.tu-berlin.de