RTP Media Congestion Avoidance M. Welzl Techniques (rmcat) S. Islam Internet-Draft S. Gjessing Intended status: Experimental University of Oslo Expires: December 16, 2013 June 14, 2013 Coupled congestion control for RTP media draft-welzl-rmcat-coupled-cc-01 Abstract When multiple congestion controlled RTP sessions traverse the same network bottleneck, it can be beneficial to combine their controls such that the total on-the-wire behavior is improved. This document describes such a method for flows that have the same sender, in a way that is as flexible and simple as possible while minimizing the amount of changes needed to existing RTP applications. Status of this Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on December 16, 2013. Copyright Notice Copyright (c) 2013 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of Welzl, et al. Expires December 16, 2013 [Page 1] Internet-Draft Coupled congestion control for RTP media June 2013 the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 4 4. Architectural overview . . . . . . . . . . . . . . . . . . . . 5 5. Roles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.1. SBD . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.2. FSE . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.3. Flows . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.3.1. Example algorithm . . . . . . . . . . . . . . . . . . 7 5.3.2. Example operation . . . . . . . . . . . . . . . . . . 10 6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 14 7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 14 8. Security Considerations . . . . . . . . . . . . . . . . . . . 14 9. References . . . . . . . . . . . . . . . . . . . . . . . . . . 15 9.1. Normative References . . . . . . . . . . . . . . . . . . . 15 9.2. Informative References . . . . . . . . . . . . . . . . . . 15 Appendix A. Changes from -00 to -01 . . . . . . . . . . . . . . . 15 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 15 Welzl, et al. Expires December 16, 2013 [Page 2] Internet-Draft Coupled congestion control for RTP media June 2013 1. Introduction When there is enough data to send, a congestion controller must increase its sending rate until the path's capacity has been reached; depending on the controller, sometimes the rate is increased further, until packets are ECN-marked or dropped. This process inevitably creates undesirable queuing delay -- an effect that is amplified when multiple congestion controlled connections traverse the same network bottleneck. When such connections originate from the same host, it would therefore be ideal to use only one single sender-side congestion controller which determines the overall allowed sending rate, and then use a local scheduler to assign a proportion of this rate to each RTP session. This way, priorities could also be implemented quite easily, as a function of the scheduler; honoring user-specified priorities is, for example, required by rtcweb [rtcweb-usecases]. The Congestion Manager (CM) [RFC3124] provides a single congestion controller with a scheduling function just as described above. It is hard to implement because it requires an additional congestion controller and removes all per-connection congestion control functionality, which is quite a significant change to existing RTP based applications. This document presents a method that is easier to implement than the CM and also requires less significant changes to existing RTP based applications. It attempts to roughly approximate the CM behavior by sharing information between existing congestion controllers, akin to "Ensemble Sharing" in [RFC2140]. 2. Definitions The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119]. Available Bandwidth: The available bandwidth is the nominal link capacity minus the amount of traffic that traversed the link during a certain time interval, divided by that time interval. Bottleneck: The first link with the smallest available bandwidth along the path between a sender and receiver. Flow: A flow is the entity that congestion control is operating on. It could, for example, be a transport layer connection, an RTP session, or a subsession that is multiplexed onto a single RTP Welzl, et al. Expires December 16, 2013 [Page 3] Internet-Draft Coupled congestion control for RTP media June 2013 session together with other subsessions. Flow Group Identifier (FGI): A unique identifier for each subset of flows that is limited by a common bottleneck. Flow State Exchange (FSE): The entity that maintains information that is exchanged between flows. Flow Group (FG): A group of flows having the same FGI. Shared Bottleneck Detection (SBD): The entity that determines which flows traverse the same bottleneck in the network, or the process of doing so. 3. Limitations Sender-side only: Coupled congestion control as described here only operates inside a single host on the sender side. This is because, irrespective of where the major decisions for congestion control are taken, the sender of a flow needs to eventually decide the transmission rate. Additionally, the necessary information about how much data an application can currently send on a flow is typically only available at the sender side, making the sender an obvious choice for placement of the elements and mechanisms described here. It is recognized that flows that have different senders but the same receiver, or different senders and different receivers can also share a bottleneck; such scenarios have been omitted for simplicity, and could be incorporated in future versions of this document. Note that limiting the flows on which coupled congestion control operates merely limits the benefits derived from the mechanism. Shared bottlenecks do not change quickly: As per the definition above, a bottleneck depends on cross traffic, and since such traffic can heavily fluctuate, bottlenecks can change at a high frequency (e.g., there can be oscillation between two or more links). This means that, when flows are partially routed along different paths, they may quickly change between sharing and not sharing a bottleneck. For simplicity, here it is assumed that a shared bottleneck is valid for a time interval that is significantly longer than the interval at which congestion controllers operate. Note that, Welzl, et al. Expires December 16, 2013 [Page 4] Internet-Draft Coupled congestion control for RTP media June 2013 for the only SBD mechanism defined in this document (multiplexing on the same five-tuple), the notion of a shared bottleneck stays correct even in the presence of fast traffic fluctuations: since all flows that are assumed to share a bottleneck are routed in the same way, if the bottleneck changes, it will still be shared. 4. Architectural overview Figure 1 shows the elements of the architecture for coupled congestion control: the Flow State Exchange (FSE), Shared Bottleneck Detection (SBD) and Flows. The FSE is a storage element. It is passive in that it does not actively initiate communication with flows and the SBD; its only active role is internal state maintenance (e.g., an implementation could use soft state to remove a flow's data after long periods of inactivity). Every time a flow's congestion control mechanism would normally update its sending rate, the flow instead updates information in the FSE and performs a query on the FSE, leading to a sending rate that can be different from what the congestion controller originally determined. Using information about/from the currently active flows, SBD updates the FSE with the correct Flow State Identifiers (FSIs). ------- <--- Flow 1 | FSE | <--- Flow 2 .. ------- <--- .. Flow N ^ | | ------- | | SBD | <-------| ------- Figure 1: Coupled congestion control architecture Since everything shown in Figure 1 is assumed to operate on a single host (the sender) only, this document only describes aspects that have an influence on the resulting on-the-wire behavior. It does, for instance, not define how many bits must be used to represent FSIs, or in which way the entities communicate. Implementations can take various forms: for instance, all the elements in the figure could be implemented within a single application, thereby operating on flows generated by that application only. Another alternative could be to implement both the FSE and SBD together in a separate process which different applications communicate with via some form Welzl, et al. Expires December 16, 2013 [Page 5] Internet-Draft Coupled congestion control for RTP media June 2013 of Inter-Process Communication (IPC). Such an implementation would extend the scope to flows generated by multiple applications. The FSE and SBD could also be included in the Operating System kernel. 5. Roles This section gives an overview of the roles of the elements of coupled congestion control, and provides an example of how coupled congestion control can operate. 5.1. SBD SBD uses knowledge about the flows to determine which flows belong in the same Flow Group (FG), and assigns FGIs accordingly. This knowledge can be derived from measurements, by considering correlations among measured delay and loss as an indication of a shared bottleneck, or it can be based on the simple assumption that packets sharing the same five-tuple (IP source and destination address, protocol, and transport layer port number pair) and having the same Differentiated Services Code Point (DSCP) in the IP header are typically treated in the same way along the path. The latter method is the only one specified in this document: SBD MAY consider all flows that use the same five-tuple and DSCP to belong to the same FG. This classification applies to certain tunnels, or RTP flows that are multiplexed over one transport (cf. [transport-multiplex]). In one way or another, such multiplexing will probably be recommended for use with rtcweb [rtcweb-rtp-usage]. 5.2. FSE The FSE contains a list of all flows that have registered with it. For each flow, it stores: o a unique flow number to identify the flow o the FGI of the FG that it belongs to (based on the definitions in this document, a flow has only one bottleneck, and can therefore be in only one FG) o a priority P, which here is assumed to be represented as a floating point number in the range from 0.1 (unimportant) to 1 (very important). A negative value is used to indicate that a flow has terminated. o The calculated rate CR, i.e. the rate that was most recently calculated by the flow's congestion controller. Welzl, et al. Expires December 16, 2013 [Page 6] Internet-Draft Coupled congestion control for RTP media June 2013 o The desired rate DR. This can be smaller than the calculated rate if the application feeding into the flow has less data to send than the congestion controller would allow. In case of a greedy flow, DR must be set to CR received from the flow's congestion module. In the FSE, each FG contains one static variable S_CR which is meant to be the sum of the calculated rates of all flows in the same FG (including the flow itself). This value is used to calculate the sending rate. In the algorithm given in the next section, it is limited to increase or decrease as conservatively as a flow's congestion controller decides in order to prohibit sudden rate jumps. The FSE also contains one static variable per FG called TLO (Total Leftover Rate -- used to let a flow 'take' bandwidth from non-greedy or terminated flows) which is initialized to 0. The information listed here is enough to implement the sample flow algorithm given below. FSE implementations could easily be extended to store, e.g., a flow's current sending rate for statistics gathering or future potential optimizations. 5.3. Flows Flows register themselves with SBD and FSE when they start, deregister from the FSE when they stop, and carry out an UPDATE function call every time their congestion controller calculates a new sending rate. Via UPDATE, they provide the newly calculated rate and the desired rate (less than the calculated rate in case of non-greedy flows, the same otherwise). UPDATE returns a rate that should be used instead of the rate that the congestion controller has determined. Below, an example algorithm is described. While other algorithms could be used instead, the same algorithm must be applied to all flows. The way the algorithm is described here, the operations are carried out by the flows, but they are the same for all flows. This means that the algorithm could, for example, be implemented in a library that provides registration, deregistration functions and the UPDATE function. To minimize the number of changes to existing applications, one could, however, also embed this functionality in the FSE element. 5.3.1. Example algorithm Welzl, et al. Expires December 16, 2013 [Page 7] Internet-Draft Coupled congestion control for RTP media June 2013 (1) When a flow f starts, it registers itself with SBD and the FSE. CR and DR are initialized with the congestion controller's initial rate. SBD will assign the correct FGI. When a flow is assigned an FGI, it adds its CR to S_CR. (2) When a flow f stops, it sets its DR to 0 and sets P to -1. (3) Every time the congestion controller of the flow f determines a new sending rate new_CR, assuming the flow's new desired rate new_DR to be "infinity" in case of a greedy flow with an unknown maximum rate, the flow calls UPDATE, which carries out the tasks listed below to derive the flow's new sending rate, Rate. A flow's UPDATE function uses a few local (i.e. per-flow) temporary variables, which are all initialized to 0: DELTA, new_S_CR and S_P. (a) For all the flows in its FG (including itself), it calculates the sum of all the calculated rates, new_S_CR. Then it calculates the difference between CR(f) and new_CR, DELTA. for all flows i in FG do new_S_CR = new_S_CR + CR(i) end for DELTA = new_CR - CR(f) (b) It updates S_CR, CR(f) and DR(f). CR(f) = new_CR if DELTA > 0 then // the flow's rate has increased S_CR = S_CR + DELTA else if DELTA < 0 then S_CR = new_S_CR + DELTA end if DR(f) = min(new_DR,CR(f)) (c) It calculates the leftover rate TLO, removes the terminated flows from the FSE and calculates the sum of all the priorities, S_P. Welzl, et al. Expires December 16, 2013 [Page 8] Internet-Draft Coupled congestion control for RTP media June 2013 for all flows i in FG do if P(i)<0 then delete flow else S_P = S_P + P(i) end if end for if DR(f) < CR(f) then TLO = TLO + (P(f)/S_P) * S_CR - DR(f)) end if (d) It calculates the sending rate, Rate. Rate = min(new_DR, (P(f)*S_CR)/S_P + TLO) if Rate != new_DR and TLO > 0 then TLO = 0 // f has 'taken' TLO end if (e) It updates DR(f) and CR(f) with Rate. if Rate > DR(f) then DR(f) = Rate end if CR(f) = Rate The goals of the flow algorithm are to achieve prioritization, improve network utilization in the face of non-greedy flows, and impose limits on the increase behavior such that the negative impact of multiple flows trying to increase their rate together is minimized. It does that by assigning a flow a sending rate that may not be what the flow's congestion controller expected. It therefore builds on the assumption that no significant inefficiencies arise from temporary non-greedy behavior or from quickly jumping to a rate that is higher than the congestion controller intended. How problematic these issues really are depends on the controllers in use and requires careful per-controller experimentation. The coupled congestion control mechanism described here also does not require all controllers to be equal; effects of heterogeneous controllers, or homogeneous controllers being in different states, are also subject to experimentation. This algorithm gives all the leftover rate of non-greedy flows to the first flow that updates its sending rate, provided that this flow needs it all (otherwise, its own leftover rate can be taken by the next flow that updates its rate). Other policies could be applied, Welzl, et al. Expires December 16, 2013 [Page 9] Internet-Draft Coupled congestion control for RTP media June 2013 e.g. to divide the leftover rate of a flow equally among all other flows in the FGI. 5.3.2. Example operation In order to illustrate the operation of the coupled congestion control algorithm, this section presents a toy example of two flows that use it. Let us assume that both flows traverse a common 10 Mbit/s bottleneck and use a simplistic congestion controller that starts out with 1 Mbit/s, increases its rate by 1 Mbit/s in the absence of congestion and decreases it by 2 Mbit/s in the presence of congestion. For simplicity, flows are assumed to always operate in a round-robin fashion. Rate numbers below without units are assumed to be in Mbit/s. For illustration purposes, the actual sending rate is also shown for every flow in FSE diagrams even though it is not really stored in the FSE. Flow #1 begins. It is greedy and considers itself to have top priority. This is the FSE after the flow algorithm's step 1: -------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 1 | 1 | 1 | -------------------------------------- S_CR = 1, TLO = 0 Its congestion controller gradually increases its rate. Eventually, at some point, the FSE should look like this: -------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 10 | 10 | 10 | -------------------------------------- S_CR = 10, TLO = 0 Now another flow joins. It is also greedy, and has a lower priority (0.5): Welzl, et al. Expires December 16, 2013 [Page 10] Internet-Draft Coupled congestion control for RTP media June 2013 ---------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 10 | 10 | 10 | | 2 | 1 | 0.5 | 1 | 1 | 1 | ---------------------------------------- S_CR = 11, TLO = 0 Now assume that the first flow updates its rate to 8, because the total sending rate of 11 exceeds the total capacity. Let us take a closer look at what happens in step 3 of the flow algorithm. new_CR = 8. new_DR = infinity. 3 a) new_S_CR = 11; DELTA = 8 - 10 = -2. 3 b) CR(f) = 8. DELTA is negative, hence S_CR = 9; DR(f) = 8. 3 c) S_P = 1.5. 3 d) new sending rate = min(infinity, 1/1.5 * 9 + 0) = 6. 3 e) CR(f) = 6. The resulting FSE looks as follows: ---------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 6 | 8 | 6 | | 2 | 1 | 0.5 | 1 | 1 | 1 | ---------------------------------------- S_CR = 9, TLO = 0 The effect is that flow #1 is sending with 6 Mbit/s instead of the 8 Mbit/s that the congestion controller derived. Let us now assume that flow #2 updates its rate. Its congestion controller detects that the network is not fully saturated (the actual total sending rate is 6+1=7) and increases its rate. Welzl, et al. Expires December 16, 2013 [Page 11] Internet-Draft Coupled congestion control for RTP media June 2013 new_CR=2. new_DR = infinity. 3 a) new_S_CR = 7; DELTA = 2 - 1 = 1. 3 b) CR(f) = 2. DELTA is positive, hence S_CR = 9 + 1 = 10; DR(f) = 2. 3 c) S_P = 1.5. 3 d) new sending rate = min(infinity, 0.5/1.5 * 10 + 0) = 3.33. 3 e) DR(f) = CR(f) = 3.33. The resulting FSE looks as follows: ---------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 6 | 8 | 6 | | 2 | 1 | 0.5 | 3.33 | 3.33 | 3.33 | ---------------------------------------- S_CR = 10, TLO = 0 The effect is that flow #2 is now sending with 3.33 Mbit/s, which is close to half of the rate of flow #1 and leads to a total utilization of 6(#1) + 3.33(#2) = 9.33 Mbit/s. Flow #2's congestion controller has increased its rate faster than the controller actually expected. Now, flow #1 updates its rate. Its congestion controller detects that the network is not fully saturated and increases its rate. Additionally, the application feeding into flow #1 limits the flow's sending rate to at most 2 Mbit/s. new_CR=7. new_DR=2. 3 a) new_S_CR = 9.33; DELTA = 1. 3 b) CR(f) = 7, DELTA is positive, hence S_CR = 10 + 1 = 11; DR = min(2, 7) = 2. 3 c) S_P = 1.5; DR(f) < CR(f), hence TLO = 1/1.5 * 11 - 2 = 5.33. 3 d) new sending rate = min(2, 1/1.5 * 11 + 5.33) = 2. 3 e) CR(f) = 2. The resulting FSE looks as follows: ---------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 2 | 2 | 2 | | 2 | 1 | 0.5 | 3.33 | 3.33 | 3.33 | ---------------------------------------- S_CR = 11, TLO = 5.33 Welzl, et al. Expires December 16, 2013 [Page 12] Internet-Draft Coupled congestion control for RTP media June 2013 Now, the total rate of the two flows is 2 + 3.33 = 5.33 Mbit/s, i.e. the network is significantly underutilized due to the limitation of flow #1. Flow #2 updates its rate. Its congestion controller detects that the network is not fully saturated and increases its rate. new_CR=4.33. new_DR = infinity. 3 a) new_S_CR = 5.33; DELTA = 1. 3 b) CR(f) = 4.33. DELTA is positive, hence S_CR = 12; DR(f) = 4.33. 3 c) S_P = 1.5. 3 d) new sending rate: min(infinity, 0.5/1.5 * 12 + 5.33 ) = 9.33. 3 e) CR(f) = 9.33, DR(f) = 9.33. The resulting FSE looks as follows: ---------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 1 | 1 | 1 | 2 | 2 | 2 | | 2 | 1 | 0.5 | 9.33 | 9.33 | 9.33 | ---------------------------------------- S_CR = 12, TLO = 0 Now, the total rate of the two flows is 2 + 9.33 = 11.33 Mbit/s. Finally, flow #1 terminates. It sets P to -1 and DR to 0. Let us assume that it terminated late enough for flow #2 to still experience the network in a congested state, i.e. flow #2 decreases its rate in the next iteration. new_CR = 7.33. new_DR = infinity. 3 a) new_S_CR = 11.33; DELTA = -2. 3 b) CR(f) = 7.33. DELTA is negative, hence S_CR = 9.33; DR(f) = 7.33. 3 c) Flow 1 has P = -1, hence it is deleted from the FSE. S_P = 0.5. 3 d) new sending rate: min(infinity, 0.5/0.5*9.33 + 0) = 9.33. 3 e) CR(f) = DR(f) = 9.33. The resulting FSE looks as follows: ---------------------------------------- | # | FGI | P | CR | DR | Rate | | | | | | | | | 2 | 1 | 0.5 | 9.33 | 9.33 | 9.33 | ---------------------------------------- Welzl, et al. Expires December 16, 2013 [Page 13] Internet-Draft Coupled congestion control for RTP media June 2013 S_CR = 9.33, TLO = 0 6. Acknowledgements This document has benefitted from discussions with and feedback from David Hayes, Andreas Petlund, and David Ros (who also gave the FSE its name). This work was partially funded by the European Community under its Seventh Framework Programme through the Reducing Internet Transport Latency (RITE) project (ICT-317700). 7. IANA Considerations This memo includes no request to IANA. 8. Security Considerations In scenarios where the architecture described in this document is applied across applications, various cheating possibilities arise: e.g., supporting wrong values for the calculated rate, the desired rate, or the priority of a flow. In the worst case, such cheating could either prevent other flows from sending or make them send at a rate that is unreasonably large. The end result would be unfair behavior at the network bottleneck, akin to what could be achieved with any UDP based application. Hence, since this is no worse than UDP in general, there seems to be no significant harm in using this in the absence of UDP rate limiters. In the case of a single-user system, it should also be in the interest of any application programmer to give the user the best possible experience by using reasonable flow priorities or even letting the user choose them. In a multi-user system, this interest may not be given, and one could imagine the worst case of an "arms race" situation, where applications end up setting their priorities to the maximum value. If all applications do this, the end result is a fair allocation in which the priority mechanism is implicitly eliminated, and no major harm is done. 9. References Welzl, et al. Expires December 16, 2013 [Page 14] Internet-Draft Coupled congestion control for RTP media June 2013 9.1. Normative References [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. [RFC2140] Touch, J., "TCP Control Block Interdependence", RFC 2140, April 1997. [RFC3124] Balakrishnan, H. and S. Seshan, "The Congestion Manager", RFC 3124, June 2001. 9.2. Informative References [rtcweb-rtp-usage] Perkins, C., Westerlund, M., and J. Ott, "Web Real-Time Communication (WebRTC): Media Transport and Use of RTP", draft-ietf-rtcweb-rtp-usage-06.txt (work in progress), February 2013. [rtcweb-usecases] Holmberg, C., Hakansson, S., and G. Eriksson, "Web Real- Time Communication Use-cases and Requirements", draft-ietf-rtcweb-use-cases-and-requirements-10.txt (work in progress), December 2012. [transport-multiplex] Westerlund, M. and C. Perkins, "Multiple RTP Sessions on a Single Lower-Layer Transport", draft-westerlund-avtcore-transport-multiplexing-05.txt (work in progress), February 2013. Appendix A. Changes from -00 to -01 Updated the example algorithm and its operation. Authors' Addresses Michael Welzl University of Oslo PO Box 1080 Blindern Oslo, N-0316 Norway Phone: +47 22 85 24 20 Email: michawe@ifi.uio.no Welzl, et al. Expires December 16, 2013 [Page 15] Internet-Draft Coupled congestion control for RTP media June 2013 Safiqul Islam University of Oslo PO Box 1080 Blindern Oslo, N-0316 Norway Phone: +47 22 84 08 37 Email: safiquli@ifi.uio.no Stein Gjessing University of Oslo PO Box 1080 Blindern Oslo, N-0316 Norway Phone: +47 22 85 24 44 Email: steing@ifi.uio.no Welzl, et al. Expires December 16, 2013 [Page 16]