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ecification here he had some really nice examples generating code for converting dates and times simple data structures like sorted lists etc in just a few seconds many ideas were used but i was especially impressed by his mention of their work on floating point representations synthesizing programs that avoided rounding errors andreas björklund and thore husfeldt shortest two disjoint paths in polynomial time andreas gave the talk for this best paper award winner in track a the problem considered is a very simple one given an undirected graph and two pairs of vertices s1 t1 and s2 t2 find a pair of disjoint paths whose total length is minimized several problems near to this one are np hard e g minimizing the maximum of the two path lengths so placing the problem into p is the major thrust of the paper the algorithms given run in o n 11 and o n 22 time for vertex and edge disjoint paths respectively the approach of the algorithm is almost entirely matrix based focusing on solving a cycle cover problem on the input graph with self loops added to each vertex except that doesn t quite work andreas did a great job of leading us on a journey where obstacle after obstacle to the approach was eliminated many of the issues relate to the complexity of computing permanent indeed one of the major technical contributions is proving that computing the permanent of a matrix over a certain type of ring is in p in the end the necessary permanent computation is replaced with a polynomial number of determinant computations giving the large but polynomial running time in perhaps the most natural course of events someone asked after the talk whether the technique might work for the shortest three disjoint paths so natural was the question that a followup slide for the question was already prepared the conclusion was probably not but andreas posed a first problem to try in this direction given an undireced graph compute the parity of the number of cycle covers having c cycles with c divisible by 4 mitsuru kusumoto and yuichi yoshida testing forest isomorphism in the adjacency list model mitsuru started by introducing the notion of property testing on graphs computing whether the graph has a given property answering correctly at least 2 3rds of the time while using only a small number of queries on the graph in this setting even the representation of a graph as an adjacency matrix or list matters as checking whether a given edge is present takes too long with an adjacent list repesentation kusumoto and yoshida considered the problem of testing whether two forests are isomorphic it was known that in general graphs this problem requires omega sqrt n queries to the graphs and only o 1 if the graphs have bounded degree for forests they achieve an algorithm that uses only o polylog n queries and prove omega sqrt log n are needed the algorithm works by first performing a special type of partitioning of the input graph then testing whether each subgraph is isomorphic the partitioning is done in a way that ensures that if the two input graphs are significantly far away from being isomorphic then some pair of their subgraphs in their partitions are too rom aschner matthew j katz bounded angle spanning tree modeling networks with angular constraints rom gave a nicely visual talk about a problem in wireless network design in the plane the input is a set of points and the output is a euclidean minimum spanning tree mst with an additional constraint the smallest angle spanning all of the edges is at most some fixed constant b a b mst another way to think about this constraint is that the largest angle between any pair of adjacent incoming edges must be at least 2 π b for b π 3 a b mst may not even exist three points at the vertices of an equilateral triangle require at least one of the points to have two incoming edges with interior angle π 3 for b 8 π 5 the b mst is simply the minimum spanning tree as the upper degree bound of 5 on every node in an mst ensures the smallest angle spanning all of the edges is at least 2 π 2 π 5 8 π 5 finally for b 1 2 there exists a simple family of examples n 1 points placed collinearly ε distance apart and a final point distance 1 from the shared line that causes the b mst to have total weight ε n 1 1 and b mst to have total weight 1 n 1 n 1 so the non trivial b are those in the interval 1 2 8 5 pi for these aschner and katz prove both np hardness and approximation results they prove that finding the b mst for b π and b 2 π 3 are both np hard using a reduction from hamiltonian path in square and hexagonal grid graphs respectively they also achieve constant factor approximation algorithms for b π 2 π 3 π 2 the approximation algorithms use a common sequence of steps compute the mst turn the mst into a hamiltonian cycle via a tour around the boundary of the mst decompose the points into consecutive groups along the cycle for each group compute a set of edges connecting the points and minimizing total edge length connect adjacent groups using the shortest edge possible step 4 requires a careful selection of group sizes as larger groups give greater potential for shorter collections of edges but for large enough b actually connecting the points may not be possible the resulting approximation ratios are 16 and lower and can further be reduced by a neat pigeonhole argument regarding shofting the groupings along the tour canal tour and conference dinner the day concluded with a tour through the canals of copenhagen and dinner at the odd fellow palace the 2014 gödel prize was awarded to ronald fagin amnon lotem and moni naor moni gave a great historical and technical talk on the work for which they received the award including the threshold algorithm ronald fagin also spoke briefly about michael franklin the missing fourth author of the work and his role in facilitating the successful collaboration posted by luca aceto at 6 36 am no comments email this blogthis share to x share to facebook share to pinterest wednesday july 09 2014 july 8 2014 icalp review guest post by clément canonne here is a first guest post from icalp 2014 kindly written by clément canonne enjoy it this post is also available in pdf any typo or typesetting issue with the html version is my responsibility on dnf approximators for monotone boolean functions eric blais in this talk eric blais presented joint work with johan håstad rocco servedio and li yang tan concerned with boolean functions more precisely the simplest representations of functions dnf disjunctive normal form formulas for a little bit of background recall that a boolean function f 0 1 n 0 1 defined on the hypercube 2 is a dnf if it can be written as that is as an or of and s one can also see such functions as being eactly those taking value 1 on an union of subcubes if one prefers i will not argue with one a nice property of dnf formulas is that they are arguably amongst the simplest of all representations of boolean functions while formulas of depth 3 are a nightmare dnfs have been extensively studied and by now everything is known about them well almost everything indeed amidst other facts we have that theorem 1 folklore every boolean function can be computed by a dnf of size 2 n 1 theorem 2 lupanov 61 this is tight parity n needs that much theorem 3 korshunov 81 kuznetsov 83 a random boolean function can be computed by dnfs of size θ 2 n log n and requires that much so are we done yet the mere presence of eric in the auditorium was a clear hint that all was not settled and as it turns out if the picture is well understood for exact computation of boolean functions by dnfs what about approximate representation of a function that is what about the size required to approximate a boolean function by a dnf if one allows error ε as a fraction of the inputs this leads to the notion of dnf approximator complexity and here again some results much more recent results theorem 4 blais tan 13 every boolean function can be approximated by a dnf of size o 2 n log n furthermore our all friend parity n only needs dnf size o 2 1 2ε n that s way better than 2 n 1 so again are we done here and again not quite this brings us to the main point of the paper namely what about monotone functions can they be computed more efficiently approximated more efficiently recall that a boolean function f is monotone if x y implies f x f y where is the coordinate wise partial order on bit strings as a starter no theorem 5 folklore every monotone boolean function can be computed by a dnf of size o 2 n n 1 2 using subcubes rooted on each min term and again this is tight for parity furthermore and quite intuitively using negations does not buy you anything to compute a monotone function and why should it indeed theorem 6 quine 54 to compute monotone boolean functions monotone dnfs are the best amongst dnfs not surprising i suppose well it s a whole new game when one one again asks only for approximations and that s the gist of the paper presented here first of all drastic savings in the size of the formulas theorem 7 blais hastad servedio tan 14 every monotone boolean function can be approximated by a dnf of size o 2 n 2 ω n 1 2 eric gave a high level view of the proof again it works by considering the subcubes rooted on each min term but in two steps regularity lemma the world would be much simpler if all subcubes were rooted on the same level of the hypercube so first reduce it to this case writing f f 1 f k each f i has this property then approximate independently each f i using a probabilistic argument via random sampling to prove there exists a good approximator for all f i s and then stitching them together and they also show it is tight this time with the majority function maj n the proof goes by a counting argument and concentration of measure on the hypercube every or almost every input is on the middle belt of the hypercube but each subcube thus has to be rooted there and each cannot cover too much so many are needed so approximation does buy us a lot but clearly using negations shouldn t should it why would allowing non monotone dnf s to approximate monotone functions ever help hint it does yep theorem 8 blais hastad servedio tan 14 for every n there exists ε n and f 0 1 6n 0 1 such that f can be ε n approximated by dnfs of size o n any monotone dnf ε n approximating f must have size ω n 2 take that intuition the upshot exact computation and approximate computation have intrinsically very different properties eric then concluded with an open question namely how to improve better understand the gap between approximating functions with monotone dnf vs approximating them with general dnf s the currently known gap in the size being quite huge almost exponential additionally how to get a separation as in the mind boggling theorem above but changing the quantifiers that is for a constant ε independent of n also can someone fix my intuition i think it s broken 1 http www cs columbia edu rocco papers icalp14 html 2 not this one posted by luca aceto at 9 44 pm no comments email this blogthis share to x share to facebook share to pinterest day 1 of icalp 2014 guest post by andrew winslow andrew winslow was one of the colleagues who kindly answered my call for guest bloggers from icalp 2014 here is guest post on the first conference day enjoy it conference welcome local organizing committee chair thore husfeldt kicked off icalp by mentioning a few stats about it university of copenhagen itu where the conference is located started in 1999 2000 students 10 theory cs faculty mostly working in track b areas in icalp parlance 1 building he also noted that itu is separate from two other universities in copenhagen hosting tcs conferences this month copenhagen university hosting sea last week and technical university of denmark hosting swat last week invited talk claire matthieu claire presented work entitled homophily and the emergence of a glass ceiling effect in social networks joint work with chen avin zvi lotker barbara keller david peleg and yvonne ann pignolet she started the talk by asking why there s only one female danish scientist inge lehmann listed on the wikipedia page for famous danish scientists out of about 60 entries why so rare looking at the dblp database data as a social network with co authorship edges gives similarly bleak results the induced subgraphs of men and women in the top 1000 nodes shows a large well connected graph and a disconnected sparse graph respectively claire and co authors developed a formal model of growing co authorship social networks including assumptions about what a glass ceiling effect means for these networks and proved that three properties are minimal sufficient set of properties to imply the effect these properties are preferential attachment a rich get richer effect where incoming students choose to work an advisor with probability proportional to the number of co authors the advisor has minority an incoming student is female with probability r 0 5 homophily students stick with an advisor of the same gender with probability 1 otherwise find a new advisor with probability p 1 incoming students are iteratively added to the graph to form growing random graphs repeatedly chosing new advisors according to homophily and preferential attachment the glass ceiling effect is defined by looking at all nodes with degree k where k k n chosen so that the number of such nodes goes to infinity with n and examining the ratio of women to men in this set if the expected ratio of female over male nodes goes to 0 as the number of nodes goes to infinity then the system is said to have a glass ceiling effect for the parameters r p chosen they are able to prove that the above three properties imply the class ceiling effect and removing any one of them does not the model was also verified experimentally using the dblp database as a final twist claire considered modifying the model to account to capture the men are intrinsically better hypothesis giving new male students two advisors rather than one this was proven not to cause the glass ceiling effect i was really struck by the meta ness of the talk and how natural the problem seems in the formal study of social networks isn t the most natural network of study the one that directly impacts our ability to formally study networks györgy dósa and jiří sgall optimal analysis of best fit bin packing dösa and sgall complete the analysis of two classic online algorithms for the standard bin packing problem given a collection of items specified by numbers in 0 1 assign these items to the fewest number of bins where each bin has an item total of at most 1 the two algorithms first fit and best fit process the items one by one placing each item permanently into an existing bin if possible otherwise placing the item into a newly created bin first fit and best fit differ only in the criteria by which they place item into existing bins using the oldest bin first f...
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