Scattering and Sparse Partitions, and their Applications

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Scattering and Sparse Partitions, and their Applications
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my name is our officer and they will tell you what's causing stress positions and the applications the sculpture will be sold traversed the following such as first without any conditions that will go straight for show the uk and only then will really.
the stands in the five the state officials will try to convince you that there are interesting and worst study so let's study. the first occasion the little styles problem here have interceptor rate point here you can define center want to send some message to some subset there are also quite probable cause your once he should seize the set of and comments can simply send the message using the same.
the edges hear the cost of sending the message is a weight off all the ages the shield in order to send this message. with these problems are fixed obviously the emotion will be many more style treat spending the center for all the clients now let's put a time when we arrive some new set of questions and that center want to send them to get the message so we can get the computer. you mean century and send the message using these which is here so this is going to the conclusion by from competitive you very costly so of course we cannot sing taken cubicle century because of course mention a fee but still you have a lot of a different message is the third time. the only solution is the universal century so here are given a single tree spending the entire graph so for example to write for the drudgery here and then once a set of a client's ride that holds enormous that simply wasn't the message in the subject read spinning always class. the green tree here and there was not set of plans to ride again was increase in the air. mrs using this. south korea saying that. so this is getting very efficient because they can do it in this beautiful setting and is one other thing is well because very simple should just had a tree and you computing sultry however might be much worse than the optimal solution and the we find the stretch of several scientific its kind of the.
worst case a performance of such a tree which is the ratio which you go over all the stops of kate moss and look on the ratio between their the new solution but the real treat to the optimal solution surprising part is actually it is possible to continue to treat such a special we not very specific.
typically jade our show the for it so both drugs she admits. even without sparse protection scheme so we'll soon find this month then you can construct a solution to the royal society problem with rage which is poor normally are thousand sigma times. ok so this is the first occasion if you have populations they have good solutions than russell central problem. this occasion or talk about is the star put real problem so here we given some with a grouchy.
the years and have some sort of the sterile state of size smoking is fixed amount to go struck in new gruff was all the turtles its critics. to preserve their properties real growth in the two following a mother's first want to preserve the geometry of the real growth respect to terrell's that is one that the system so he'll be this as an initial spend this is not a for every pair of to austin the price will be at least as large as a. pieces of the rugby as most of four times larger little she's doing the regional the usual sense preserving the geometry of the original draft and secondly i wanted the a graph will be a minor of the businesses all to preserve the closure of the rocky so if she was playing for example new professional people. also player. and the golf course is to minimize our so here's one example suppose of the same star gruff year air always around the city centre point you start a point which means i don't know or two weeks after all and the only way you can get the mind of his own internal such a certain extent is the contracting one of the ages. so get his rough year not the weights must be at least two because you must know when a real differences and therefore these as a paean to cry it was really do now it's for so have the store should have to. and this is the best thing you can do so if you like a war about the new forest and upon removal problem. so what is known so we showed in previous paper that gift for every gruff he was content was you can construct a solution the structural problem with torsion the greeks in case the only war but his body child our show norwalk course and eight and is only knows just get between eight and locate.
please interesting however was actually more interesting is what's happening special graphic these so when you want to preserve the publicity for more police to be read have some sense but they have some special structure so if for example or your craft is plainer what you can say smarter boston as well problem and actually doctor to ending. smarter they got to steal between eight and locate is a major question who was always possible for us and other support equally restricted rough families. the shown these forty one sense the main tour of this paper that if air every jew subscription rugby that meets a stigma thousand but his team then you can construct a solution to the startle probable the store schengen where normally a towel and signal.
it's against the current positions in price. it's socially want real problem so now start response and friendly find the start of petitions.
so starting spot for the chance so here he said the petition you so these like a partition divide all the bridges in the graph the clusters sigma while those the spot where the asian if first you want to teach classes have the outer most delta.
and secondly you want every ball for fraud use though most daughter sigma so these kind of putting parameter how much work to be smaller in the right don't have enough and you want to every ball for the most goes over signal with the second most powerful astor's also have two problems here though he said. the orbiter signal is the betting thousand number of sessions and so can see that these will intersect three clusters and these bozos don't you posters and as well not his single british understood you sheer pro build the single tradition and only succeed respect to held the post children asleep. it all the kind of small ball winter said most of our clusters. considered a graph of meets the mythos party is scheme if you can construct see what our built a special edition for every health problems are healthy and if you're in bajur out with even referred me to see what our study is keen deconstruct the solution you are substantially problem with rage.
just for a number of our signal and look at. ok so you know the case again with the sheer but she's not very well the fight there are two types of the amateur people should talk about so for the week youngster so given the clustering the we jumped off a is the actual results in the original ground between two versus in a and the strong out there is the same but instead you look at the.
you have a so you can the police as we can to medicine in the new suburb so for example conceal discuss to each year so.
social graph and these are the engine stew in the new some references six. in a quarterly that we could get your face for so it does for and the strong going to have six or they might differ really might be for bailouts for example a is and connect and so the william it's are you some ball number of the strong and there isn't she. italy's week saw the amateur known to fruition of stress position you can either so say strong position or with prostitution respected in the article the until you have strong and sparse petition.
in respect to the petition to get ok so no to actually get our used weeks prostitution is going to miss a few graph of recruits first edition skin when you get solution to the real star treat but with the good as a result of using some weeks prescriptions is that the actual tree is not a subgroup so.
in the sense you get some tree but coming you cannot restricted to only use ages of the original group so if you like a graph your trip to be some rough possible using result the bush how we use some hired your suspicions but the results are much weaker and actually there are some interesting questions here which will for sure. already discussed. ok so move on to define cutting party has been so this is very similar again you have these three brothers.
and you want the following whole the first you want to be connected. secondly wanted to we don't have the car to the most they'll do says this is somewhere in between songs and we british and says records from one hand work with their mother from the other hand you want the young strong the outer to be barred not be ok so first want this kind of strange. yesterday and secondly we want to every for a spat of flats the most notorious sigma winter second most klosters not previously world war two to start small number of pastors know what a spat in the sex workers and they get sick winner says the building product are we. what is the ratio between to be out of the cluster few aid pet care about and signifies number of sessions. yes we can see this curator said three quarters is well to questions to process and so on our case away. this is a risk to patients and we say that a gruff me six thousand british a scheme if a for every youngster problem delta you can construct a stigma our goal to ask a question and the main result of this paper if every jew sawgrass and g. signal thousand british askew.
then you can construct a solution to start with real problem was torsion and how they put in on the outside. so even though this is the major of the paper. the exhibitions and don't really have been discussing instead to go it's got the politicians and so will we started because observations with a different position in the relationship in the and they will go were different graph families and the strike with a petition could be constructed they will finish with some conjectures and open question. so first air market is observed if you have a stigma our goal to stop first position is also weeks for this because of me stronger mysteries.
that's it. secondly what can observe that if you have built a strong position then also he said but it is also starting position in there is is that every first pair of a lens go to receive more than good in some ball go overseas.
so that's it. in a sense the picture of the world which combines for so we have stuttering week and superstition every some politicians also scott three week but there might be some pretty sure start with but the week began cycling about she even may be really strong only see examples of families languish want.
these places. ok so let's start as within families in the first family can ask about his trees for these the most basic family what about trees. what i'm pretty sure he could be constructed. so first we observe that you can have a stroke good strokes propositions king so you have some the bonds of don't respect the stigma there is the fourth and you can construct a gruff the tree.
i cried a high degree be a treat. and then in the cluster cannot contain country so it's much and some words of support this is the most ever take long to the cluster of the route then the most children belong to different cars but because we require strong young ish such child should go to different quarter. in there for the poll for you she was wrong as vertex will contain deepest one of these a degree klosters to start breaking to lots of cultures and his wife and you can actually paid for others is what you get so like to promising keep in mind these are for example if you want.
to preserve post a fraud use a slogan fraction of the amateur the opposite sex the slogan crofters and if you want something like a small it's the only become quite exponential so this is very bad actually does as bad as john grasp. ok so this is so conditions not working for jon hamm to co-star very good catch and petitions your soul can be with conditions can and the clustering he is very simple so first just struck the ball rug the rules and then for each share critics also said.
pfizer the cost of just a car to construct the ball on the itself and so on to have to think she was previously with small both bring to a huge number of causes these are the issue because we care and got that's here so we few have the british year was all child's goal because there is still king only one side once outside in the sea so all we can. in the second most three different clusters. king next one can also struck good weeks passed with the skin for trees and they get here is that it's ok so you cannot you might have the say the same issue but they always does or kids separate from the father and about how we can always teasing well crafted because the car. not need to become like that you can see is a connection sheer were still all these viruses have a common ancestor not far away so their heads together and all working well as well so we can put truth here so that the scuttling petition dead meat we start politicians but the law to be strong for petitions with.
the brothers again this family would discuss the family of public attention to the sun says we send a metric space has doesn't mention the every bowl for you to our can be covered the most to the are also had the right use this instance trying to a generalized clean they mention the every.
in space of the mention the has doubled to mention to clean the end. he said at the graph is a lynching the things you. as such they mention. yet all showed that the graph has the mission the then you can construct a spokesman. weeks prescriptions kim was promised one and exploration the. so it's good to hear in the show that should you can construct talks with your skin with dementia was brothers bourse. it's going to be. it was the here and know that these actually provides an explanation proven maj depends on the in this mission to be wrestled to the problem for these family of dublin commission the.
pay their bills next to me would discuss that with so we hear a is try to measure how like these is like a tree with is also has an important role and the robots will see more structured your arms.
and we a show that you can construct food stocks for position and goods weeks or tradition this implies. so if you have on the bed. we'd the supplies that you had a can of course exhibition to be reversed certain star trek. no problem with dependence which is a constant problem you grow this is the first family and if you know get some interesting solution about with some sort of political action hours early trees in some published a paper about a little grass. but citing they frighten you a get make similes any clues crofter the sense to treat cycles these kind of a.
version guess also paragraphs and we get their goods country that we petitions hoard the countries so they don't have good strong sparse petitions. next families coral reefs these graphs the english there is no induce cycle seventy four. it's a new cycle seventy four. for every you settle says his forty's coral and began a very different countries because the for example can take weeks to steal their be good in this country get recriminations and the also to preserve so there is no strong suspicion this kind of basic family so nobody suppose interesting that you can construct a strong suspicion for doubling. metrics the country's but actually there are trees which do not has in the bay. the shares and dog out with much. iraq.
and next for me would cause these days of queens specs. so even though it's in space used to construct positions so weeks propositions clear because we both the door to the politics will have reporters in the sense actually we show the day you can't do anything better than only use the fraud in his press has bought a doubling the bench. this instance the same was here able for the other hand you can construct very good starting positions so air with english conditions so in clear space for a special the sinking intervals is alive and two points and by using the scrum to read like a petition to wake you because you can show the. a get a one in the skin condition promise one could be a sense if you. even when we spoke with the scheme so she can get one less the debt is equal to the amateur if you want to get anything similar with the suspicion that number of poor a cost to the sec will be explaining show. the. first suppression here so good to clear space here in the warming they're both and on the first big difference so as its difference be putting in space a here finally biggest the most interesting family can think about in this context is the soft money for grabs.
so using the f.a. must say keep our politicians will construct the are square in to the are exposed. is keen for one free love with them. your but what about cutting so we actually don't the season. open question them into question live in what the conjecture that you can just a struggle for example for telegraph i believe that you can construct certain conditions with problem with a cross on constant.
in no to pay between quite a constant the distortion solution for this terrible problem. which is a major portion cancer with its conjecture and the final family we discuss of course is that of john rosse.
the so first jet all show with the slogan no could express which is kim. it falls by or by come by our basically the age of trust me and local look at the prestigious came in this world we couldn't find the stories also show the job last week local the drugs for these countries as his first two and we also have a war about show he is essentially tied we can sort of the skin to. you can order terse. and the only question left to robots cars and petitions so we don't have your body of evidence that you cannot get course also. yet but you can judge actually can do better his condition than this week's first edition of conjecture that you can be cost of local schools and colleges and his start in sense you can construct that's of friends about plants a video of the cost or the are second only.
the logo and partition old moving the ocean are getting into cost.
this lets about so first day we discuss the stupid of connection between their suffocation is too difficult conditions we get our ability to which was pretty is king data klyce a good solution to the sultry problem. and this work to show the every so you subtract that meets goods companies can then you can get a good solution to this problem was probably putting on a signal. when discussing a discussed.
he says and various gras families.
all the rocks picture and their daughter questions the following so first the conjecture that a rough week because of cost and scotland protection scheme which will apply course of the store she solution to starbucks will problem a conjecture also good for the family tree with graphs should get some a depends on uk in for. but the scheme. and also be conjecture the giraffe you'll meet costs of august i think putin skin so for this to her various occasions a full sample problem but for this why don't have any extra education i think is very national problem. sunday lycett hope you enjoy and green paper.