*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.

### 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.

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-fit) or bin that would have the least remaining room after the item is placed into it (best-fit). It was previously shown that for every instance with optimal solution using OPT bins, first-fit and best-fit use ceil(1.7*OPT) bins and there exist instances where both use 1.7*OPT bins. Dösa and Sgall improved the upper bound to 1.7*OPT bins, dropping the ceiling and completing the analysis of the competitive ratio of these algorithms. Jiří commented that he felt that such classic algorithms deserved a complete analysis and I agree; the talk had an air of finality, having put the 40-year-old gap to rest.### Hossein Esfandiari, Mohammadtaghi Hajiaghayi, Reza Khani, Vahid Liaghat, Hamid Mahini and Harald Räcke. Online Stochastic Reordering Buffer Scheduling.

Vahid Liaghat gave this talk on a scheduling problem where items have types from a fixed universe and enter into a buffer of sized size k. One can then process all items of a type, flushing them from a buffer and causing new items to take their place. The cost of processing a sequence of items is either the number of processing steps used (block operation model) or number of times the type processed changes (standard model). It was known that a O(loglog(k))-competitive algorithm is possible for the adversarial/worst-case. This work studies the sitation where the input is not adversarial, but is randomly sampled from some set. Esfandiari et al. achieve an average-case O(1)-competitive algorithm for both the block operation and standard models for the case where an adversary designs an input that is then randomly permuted. The analysis uses several lemmas regarding the optimal solutions of various buffer sizes as well as threshold algorithms: algorithms that process each type as soon as a specific number of occurrences of a type is exceeded.### Erik D. Demaine, Yamming Huang, Chung-Shou Liao and Kunihiko Sadakane. Canadians Should Travel Randomly.

This paper attracted a few comments related to the curious title. The title comes from the "canandian traveler problem" of study, introduced by Papadimitriou and Yannakakis in 1991. The problem is a shortest path problem with partial information : some of the edges of the path are blocked (by intense canadian snowfall) and cannot be traversed, but this is only known after a traveler has visited an endpoint of the blocked edge. The parameterized version of the problem has k blocked edges, and the goal is find an algorithm with good competitive ratio compared to the shortest path that avoids all blocked edges. For deterministic algorithms, tight 2k+1 upper and lower bounds on the ratio are known, while for randomized algorithms, only a lower bound of k+1 (and implied upper bound of 2k+1) were known.Demaine, Huang, Liao, and Sadakane improve the best-known randomized algorithm in two ways, giving a polynomial-time algorithm that achieves a ratio of (2 - o(1))k + 1, and a pseudo-polynomial-time algorithm (parameterized by k, the number of blocked edges) that achieves a (1 + sqrt(2)/2)k + 1 ratio. The ideas for both algorithms are to repeatedly compute a collection of nearly shortest paths, traverse them each until blocked, and repeating the process with the new information if none of the paths lead to reaching the destination. A careful selection of the number of paths used then yields the bound. The main difference between the two algorithms is exactly what short paths are used; the pseudo-polynomial-time algorithm uses a list of shortest paths, whereas the polynomial-time algorithm only finds paths within a constant factor of the shortest.

### Dmitry Gavinsky and Shachar Lovett. En Route to the log-rank Conjecture: New Reductions and Equivalent Formulations.

Dmitry started by reviewing two-party communication problems, where the goal is to compute a combined Boolean function f of inputs x and y held by the two parties while passing the fewest number of bits between the parties. One can consider the matrix defined by the two inputs, with an entry for every (x, y) pair, called the Boolean matrix. The rank of this matrix (and Boolean function f) is the minimum number of rectangles found in some partition of the matrix into rectangular blocks of entries with the same value. It is known that if a c-bit communication protocol is possible, then rank of the matrix is at most 2^c, i.e. the communication complexity (in bits) is bounded from below by log(rank(f)). The log-rank conjecture is that polylog(rank(f)) is an upper bound on the communication complexity of computing f.Part of this work by Gavinsky and Lovett is to provide a number of equivalent versions of the problem that may provide a way to make progress on the log-rank conjecture. For instance, they show that proving the log-rank conjecture for the randomized communication complexity on low-rank functions implies the log-rank conjecture for the deterministic version, as does proving the conjecture for the information cost of f, the minimum amount of information given by each party the other party in the worst-case.

### EATCS General Assembly

The day ended with the EATCS general assembly led by Luca Aceto and appearances by the many people involved in ICALP and EATCS. ICALP 2015 will be in Kyoto, Japan, and some information about travel, accomodations, and Kyoto were presented by Kazuo Iwama, and ICALP 2016 will be in Rome, Italy. Some statistics about ICALP 2014 were given by Elias Koutsoupias -- the number of submissions is up from previous years, acceptance rate is about steady at 30%, and the vast bulk of the submissions were to to Track A.As one final thought from the day, the organization of the conference so far has been top-notch. Many of the talks are online (including Claire Matthieu's), the sessions start and end on time, sound and projection issues are non-existent, and the food/drink is tasty (and rotates every break...).

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