>> Thank you so much for inviting me. I'd like to talk about some new understanding, on sorting circuits. We've been working on this line of work since 2017. So I'll mention the results from a few papers, to paint essentially, the frontier of our understanding. This is trying work with many wonderful collaborators. Some of these studies were also partly motivated by a somewhat different quest, that is: how to construct optimal oblivious RAM. Although, in this talk I'll mostly focus on the circuit model rather than the ORAM. At the end of the talk, however, I'll quickly mention how the circuit results are related to the optimal ORAM, and how they are not related. Like, in other words, how the circuit techniques actually depart from the techniques we use to construct optimal ORAM. I'll only have time to mention the results and you'll have to read our paper for the details. Sorting circuits have been studied for many decades. A long-standing open question in the complexity and algorithms literature is the following: Does there exist sorting circuits of o(n log n) size? So what do we know about this question? First, we know that to get anything better than (n log n), it cannot be comparison-based. Comparison-based has a well-known (n log n) lower bound. And this lower bound applies no matter whether it's the RAM model or circuit model. If we forego the comparison-based requirement, however, we know that on the RAM, sorting can be accomplished in nearly linear time. Unfortunately, these RAM algorithms, critically rely on dynamic memory axes and cannot be converted to the circuit model in a way that preserves efficiency. Okay, so we've been stuck on this question for several decades. As I mentioned, this is one of the well-known long-standing open questions in the complexity and algorithms literature. Somehow we cannot make progress either on the upper bound, and lower bound fronts. In some sense, it's almost surprising that after so many years, we still don't understand sorting circuits. So let's see why we are so stuck. On the upper bound front, we are stuck at the AKS sorting network from 1983. The AKS sorting network is comparison based, so it is actually optimal in the comparative-based model. A long-standing question is: Can we beat AKS if we forego the comparison based restriction? It turns out that we haven't made any progress at all along this front. On the lower bound side, we also seem to be pretty stuck. In fact, not only do we not know how to prove and (n log n) lower bound sorting circuits. In fact, we don't know how to prove a superlinear lower bound. And in fact, it turns out proving superlinear circuit lower bound for any problem into the n key, is beyond the reach of current techniques. Okay, despite all these long-standing barriers, we were able to make a little progress in terms of understanding sorting circuit complexity, both on the upper bound and the lower bound fronts. On the upper bound side, somewhat imprecisely speaking, we showed that sorting (n) elements, each tagged with the k-bit key can be accomplished with a circuit of size and timescale. So if, for example, K is asymptotically smaller than log n, we can actually defeat the AKS sorting network. Our result can also be viewed as a generalization of the AKS sorting circuits. And note that I'm ignoring poly log star terms in the bound. On the lower bound side, we showed that essentially the above upper bound is tight for every choice of (k), either assuming the indivisibility model or assuming the Li-Li network coding conjecture. So let me explain. The indivisibility model assumes that the element's payload strings are opaque, and the circuit does not perform any encoding or computation on the element's payload strings. And indeed, you know, almost all of the algorithms we know are, indeed, in the indivisibility model. Now the Li-Li conjecture is a well-known conjecture in the area of network coding. It posits that network coding cannot help anything beyond the standard multi-commodity flow rates in undirected graphs. So while no one knows how to prove unconditional super linear circuit low bounds, we were able to prove a conditional lower bound. And, you know, the lower bound also implies that if the Li-Li network coding conjecture is true, then one cannot build a sorting circuit of o(n log n) size for the, you know, case of general keys. So for the rest of the talk, let me say something about this upper bound and why it turns out to be very much nontrivial. In fact, it turns out that even for the 1-bit key special case, the result is very much nontrivial and there are many natural barriers towards achieving these results. So essentially in the 1-bit special keys, right, the result says we can sort 1-bit keys in the linear-sized circuits. I also want to mention that in the problem formulation, besides the 1-bit key, every element also has a payload string. And when you start, you have to carry the payload string around because otherwise had it not been the payload string, right? You could just, like, count how many ones there are, and then write down the answer. Before I talk about, you know, even why the 1-bit case has many barriers, let me actually quickly mention that the 1-bit case has a very cool implication. It implies that median can be computed in the linear-sized circuit, as well. Remember in your undergrad algorithms class, we learned the textbook Blum's algorithm for computing median on the RAM. And we know that it can be computed in linear time deterministically on the RAM. And in fact, this is one of my favorites when I teach undergrad algorithms. So you would almost expect that, I mean, of course, naturally, you should be able to do the same, you know, in the linear-sized circuit. But it turns out to be much harder than you might expect. And no one really knows how until our work. In some sense, the natural barriers for sorting 1-bit key also apply to median too. And for both of these problems, sorting 1-bit keys and median, in the circuit model, like, believe it or not, the prior best-known solution is actually AKS sorting circuits itself. And nothing better is known so far. And so to help you understand why, you know, for something so natural, like, it's so natural that if I didn't tell you it's hard, you'd almost take for granted. And, and let me explain why there are natural barriers. So the first barrier was actually described, even in Knuth's textbook from the 1970s. And, you know, the textbook said essentially, such a result would not have been possible in the comparative-based model. And the reason is because of the zero-one principle, right, so the zero-one principle is that any comparison-based sorting circuit, if it can sort zero-one keys, it can also sort general keys. So, therefore, the (n log n) lower bound for comparative-based sorting actually applies even to the 1-bit key case. Okay, well, to the best of our knowledge, our existing sorting circuit constructions indeed are in the comparison-based model. You know, it's been a natural question, like, whether we can achieve anything better using non comparison-based techniques. Nothing is known, and this is not like the RAMs model, right? In the RAM model, we know how to make use of non comparison-based techniques to get interesting results. The second barrier was actually recently shown in our own work, as well as a work by [00:09:07] and others. Okay, so it turns out for the 1-bit key special case, if you require stability in the sorting, again there's (n log n) barrier. And again, the barrier holds either assuming the indivisibility model or the Li-Li network coding conjecture. Here, stability means that for the elements with the same key, we insist that the other in the output array must respect the relative other in the input array. Okay, so to get a linear-sized sorting circuit for 1-bit keys, not only do we have to forgo the comparison-based restriction, we also have to forego stability. So finally, you know, when we overcome these barriers, and we are eventually able to construct a sorting circuit for 1-bit keys, the next question is how to upgrade it to a sorting circuit for k-bit keys. And here, we encounter another challenge. And the challenge is exactly because the 1-bit sorting circuit is not stable, right? Had it been stable, you know, a natural idea would be to use radiant sorts. But radiant sorts expects that the 1-bit sorting case, you know, is stable. So in fact, to do this upgrade, we came up with a new technique, which is like a clever two-parameter recursion technique. Okay, so I won't have time to go into details. Let me quickly comment about the techniques at a very high level. So, essentially, we start with Pippenger's self-routing super concentrator. Imprecisely speaking, if we directly converted his super concentrator construction to the circuit model, we would incur (n log n), but then we can rely on the cool observation that was actually made in the earlier work on constructing smart-depth, perfect, oblivious, parallel RAM. So in this work we observed that Pippenger's super concentrated construction actually has the online phase and the offline phase. So interestingly, the offline phase depends only on metadata, and it never looks at the element's payload strings. And also, interestingly, it's also the offline phase that's causing the (n log n). Whereas the online face is easier to implement in linear-sized circuits. So, by exploiting the fact that the offline phase operates only on metadata, we are able to use a recursive bootstrapping technique to essentially squash the (n log n) to something like (n polylog * n). So last, but not least, let me say a few words about how this is related to optimal ORAM. In optimal ORAM, we essentially need an oblivious algorithm that sorts 1-bit keys in linear time, and this is on the RAM, right? So to get that, we also rely on Pippenger's super concentrated construction, and we rely on the same offline, online insights, but then to get rid of the (n log n) in the oblivious RAM model actually almost requires, like, in some sense, the opposite techniques from the circuit model, right? So in the, on the RAM model, we know that every word has log n bits, and we can simultaneously perform log n bitwise operations in unit costs, you know, because this is like operation on a single word. So therefore on oblivious RAM, one of the core techniques we use is packing. But, you know, packing is, like, there's no free packing in the circuit model, like in a circuit model, every wire, every gate would have counted. So therefore, the algorithm tricks we use in the circuit model is actually rather different. Okay, I guess this is about as much as I can say about this line of work. To summarize, it's almost surprising that after so many years, we still don't understand sorting circuits. In fact, you know, it looks like we've been pretty stuck since 1980s. So we were able to actually push the frontier of our understanding a little bit, both in terms of upper and lower bounds. Thank you so much for your attention.

bye okay welcome back everyone this is SiliconANGLE and Mookie bonds to cube our flagship program we got the advances reconsider from the noise I'm John foreach n with Dave vellante here for just a conversation Dave about what's going on oracle openworld day one of three days of live coverage here in San Francisco what's your take dick well first of all John miss you yes I had furrier withdrawals here so welcome back them first segment we've done together all day I was out at Santa Barbara last night in checking out the scene down there made it back not going to miss an Oracle OpenWorld for the world I love a work eloping world because it's like Isla Vista in Santa Barbara except it's tech people going crazy over the technology so mas coyote is draped in Red John well different in a few weeks ago at vmworld but I mean it's always great because you know Oracle has the muscle Dave as you know we always talk about every year Oracle's so you know transitioning from that telco role of extracting value from the ecosystem Oracle's making moves Larry Ellison really is a gamer he wants to make his mark on the industry he sees himself as the heir apparent to steve jobs in the end the end the historic hall fame of tech industry and he's here to win it's a game to him and I think you see oracle just in the past four years since we've been covering them being kind of a this is a throwaway game for them to like really being in the game they're making the announcements they're heavy and cloud they're making a faster more relevant timely announcements again they're a monster they're in there a huge accounts huge dollars and a rounding number on their sales spreadsheet would take a company public these days so you know those startups are doing well Oracle still has the muscle and they have huge clients and I'm going to watch and I think you know you ask me might take perform over here a consistent story from Oracle it's engineered software engineered heart with hardware it's vertical integration it's trying to develop best to breed its spending on R&D now they've basically co-op to the Big Data theme you know we hear a lot about their cloud so you know it's fun to criticize Oracle right they charge a lot a you know coops industry terms and act like they invented it on and on but here's the deal they spent a lot of money on R&D Allison's like a start-up CEO I mean he's that engage them I resisted this session talking to some executives and in the infrastructure business and they're telling me I Larry's call me every week wants to know the update on the new product and output when it's coming when it's ready you know herds the same way so you guys are intense focus on as you said winning that is all about winning it's a zero-sum game to Oracle it's the chest it's a chess board for Larry and I think you know one of the things we're seeing some news here we had our guys at the press conference mark hurd made an announcement about the human capital management software you know they're you know it's classic Oracle swiping at the competition work day has been booming of late and you know they're under pressure you know and you know workday asli the PeopleSoft guides have a huge chip on their shoulder they're winning they're doing well and Oracle's not happy about it so I mean obviously they're going to be moving very very aggressive against that and then just in all fronts the chessboard of conversion infrastructure the Sun acquisition really the ultimate cherry on top for Oracle relative to their future positioning they are betting the ranch on an apple-like strategy where containing the hardware focusing on the software and bundling in the hardware to the software as a fully enclosed system purpose-built hardening it out is ultimately their big bet David I'm telling you it will work for some companies and that lock in is a small price to pay for the functionality if they can deliver well and I think they I think Oracle can deliver you know the question is is as we're talking about with ray Wang can they deliver both on the promise of integrated systems I have no doubt Oracle can do that because they're spending a lot of money on it they got good technology people they've got good technology and and so eventually they're going to make that integration play work and they already are making Network the big question I have John is can they innovate and be best to breed at each layer of the stack that's something that's really hard to do guys like EMC and Cisco and VMware have chosen to partner to do that that's always been IBM's big challenge right i mean what's IBM number one at what product is IBM number one besides mainframes it's hard to come up with one okay then same question of Oracle what product is Oracle number one at besides database that's Oracle's challenge you know can they be best in storage can they be best in servers can they be best in applications they would argue their best in applications and I think big date is a big challenge here we heard inside the cube here day one that people don't want to pay licenses for data that's not being used and there's a big issue around the how data works how people using their computing environment it's not a monolithic environment anymore relative to the database there's new unstructured environments most of the data is not stored in relational databases why should I pay an Oracle lights of them I got virtualization I got scale-out open source these are new environments that are putting great pressure on Oracle and if you look at Mark Hurd and how he reports to the street all he talks about is our revenues licenses are up x percent barrel tins of the market well if demarcus declining and you're up what does that mean maybe this shifting to another area so Dave this is a concern that I have about Oracle is their core business metrics might not be on the right numbers yes software's growing relative to what I'm a declining market or shifting market those are the open questions we will find out this backdoor I think that well here's here's something I want to share with you so we did some wheat research and Wikibon fifty percent of the customers that we talked to in the Wikibon community said they're willing to risk lock-in to get integration and function so then and only fifteen percent said we're dogmatic about open source now over time that open source crowd as you well know is going to build up the capabilities but fifteen percent is the toehold for the start of startup crowd Oracle's working on that fat middle and that's really where they do let's talk about the dogmen the dogma for IT enterprises simply there's contract negotiations all posturing for contract negotiations almost every single CIO I talk to and we've talked to Dave have either told us publicly and privately hey at the end of the day I care about the cost structure the environment and to if there's a hardened top unlock in it doesn't it's irrelevant then and the example that we've always using the cube is you the Intel microprocessor do you really care about the proprietary software involved in an Intel processor no just gets the job done and it enables other things that's the key question that we're looking at right now in the computer industry is where is that hardened environment where being collapse elation of the complexity has been taken away to the point where it's absolutely functional that is ultimately to be the key and I think that's going to have to enable data fabric layer and then top of stack of applications I think that's a VMware strategy is a good one I think of Oracle can pull that off they could be the Intel of this cloud error well the other big battle is the organizational battle because Oracle obviously sells the dbas and application heads and everybody else in the hardware business sells to infrastructure people and let's face it the dba's and the application heads have all the juice in the marketplace so that's those guys are driving the buying decisions now as companies like VMware become more strategic they can maybe get some access to those individuals but still Oracle an essay p own that it all you do skoda you go to sa p sapphire you come to oracle openworld a lot of suits you go to emc world and you're seeing you know a lot of infrastructure people so that's a big battle that people taking on but i would if i'm a customer i would absolutely have some alternative infrastructure around wouldn't go just all red stack there might be some situations where i want to do that i guess the point I'm making is a lot of the application heads don't care if they spend more on infrastructure they don't care if they get locked in because they care about how fast the application runs how easy it is deploy how agile it is what their service experience is like that's what they care about I think ultimately it's going to come down at ability to be flexible have the application support so Oracle obviously will have the ability in most their companies to do that the question is do they have the right product mix and I think giving the customer's choice that's what we've seen with OpenStack in particular and you look at OpenStack what that's done is given this choice to the enterprise's to do whatever they want relative to having a private and public and hybrid cloud environment and that's ultimately going to help with the kind of the choice option so I mean that's kind of we've heard Oracle's portfolio or has got one of everything we heard you were in the cards so you didn't hear Thomas curing this morning but I mean you would have thought they were invent big data I mean it was a dupe connectors in-memory databases you're talking oh you know no sequel key value stores we got at all and they do actually have a lot of that hey so the portfolio is very robust they can tick the boxes they can they can play that functionality game with anybody and the real advantages they talk to the CIO now over here you've got the walk-off the marc andreessen crowd right none of my startups by Oracle hey stuff so it's those guys it's the open source crowd that ultimately is going to get leverage in the marketplace and you know John you and I have talked about this in the cube a lot ultimately long term open source wins Gary Blum was on the cube earlier CEO of now CEO president MarkLogic Dave he's been a I think 17 years of Oracle insane amount of years he's been there from the beginning he goes back to veritas as well you know he had an interesting point he said that in MarkLogic they have a half a DBA for ten dba's that are on staff for oracle that's a nine and a half labor pool reduction in cost and you're granted some of those guys might retire kind of like mainframe guys in the old days but like still you don't know about a massive amount of restricting of resources I want to get your take on the data economy type role I mean the data economy we're talking about new economics what's your take on I mean that ratio is really the kind of magnitude we're seeing relative the big data so here's my take on that is is I think that rightly so the startups are doing what Larry always does he compares his state of the art to somebody else's n minus 2 and that's what the startups are doing right there's a lot of legacy Oracle environments very easy to go in and say okay I can reduce your operating expense here's the challenge Oracle knows this and they see that threat so what Oracle's trying to do is is is cut that you know to whatever degree it can cut that and and close that gap and then you know have the cios bet on oracle because their quote unquote less risky right nobody ever get fired for bringing on IBM so the game that they have to play I heard Gary say we have a five-year lead on the competition so it's like fusion-io and EMC right EMC it lead on on emc we had packed LC on the QB said hey we're behind we're going to catch up how did they catch up they went out and they bought a company now I haven't caught up yet but they went out bought a company they started investing R&D but they're closing that gap and so that's the game that they play okay we're here inside the cube this is SiliconANGLE Yvonne's coverage of the cube stay with us we're going to be going to come back with Jeff Kelly Dave next we have any more guests coming in we're done this is a wrap for the day okay we'll be back tomorrow on Tuesday stay here SiliconANGLE guns the cue our flagship program day one wrap up here at Oracle OpenWorld yes my goal she's coming on we got a bunch of guys coming on from emc emc has 80,000 oracle customers oracle itself says it has 40,000 hardware customers so that's going to be an interesting we want having a special thanks out the qlogic for letting us stay in their booth again fourth consecutive year the legacy SiliconANGLE and CNBC are broadcasting live here at oracle openworld this is day one coverage with new Act tomorrow with the keynote in the middle of the afternoon all day coverage starting at nine at ten o'clock tomorrow morning here from the cube stay with us and see you tomorrow