In a social network, nodes correspond topeople or other social entities, and edges correspond to social links between them. In an effort to preserve privacy, the practice of anonymization replaces names with meaningless unique identifiers. We describe a family of attacks such that even from a single anonymized copy of a social network, it is possible for an adversary to learn whether edges exist or not between specific targeted pairs of nodes.

https://www.cs.cornell.edu/~lars/www07-anon.pdf

Wherefore art thou r3579x?: anonymized social networks, hidden patterns, and structural steganography

A q-query Locally Decodable Code (LDC) encodes an n-bit message x as an N-bit codeword C(x), such that one can probabilistically recover any bit xi of the message by querying only q bits of the codeword C(x), even after some constant fraction of codeword bits has been corrupted.We give new constructions of three query LDCs of vastly shorter length than that of previous constructions. Specifically, given any Mersenne prime p = 2t − 1, we design three query LDCs of length N = exp(O(n1/t)), for every n. Based on the largest known Mersenne prime, this translates to a length of less than exp(O(n10 − 7)) compared to exp(O(n1/2)) in the previous constructions. It has often been conjectured that there are infinitely many Mersenne primes. Under this conjecture, our constructions yield three query locally decodable codes of length N = exp(nO(1/log log n)) for infinitely many n.We also obtain analogous improvements for Private Information Retrieval (PIR) schemes. We give 3-server PIR schemes with communication complexity of O(n10 − 7) to access an n-bit database, compared to the previous best scheme with complexity O(n1/5.25). Assuming again that there are infinitely many Mersenne primes, we get 3-server PIR schemes of communication complexity nO(1/log logn)) for infinitely many n.Previous families of LDCs and PIR schemes were based on the properties of low-degree multivariate polynomials over finite fields. Our constructions are completely different and are obtained by constructing a large number of vectors in a small dimensional vector space whose inner products are restricted to lie in an algebraically nice set.

/pdf/towards-3-query-locally-decodable-codes-of-subexponential-3kj282s4d2.pdf

Towards 3-query locally decodable codes of subexponential length

Preliminary Definitions, Results and Motivation Stable Matching Problems: The Stable Marriage Problem: An Update SM and HR with Indifference The Stable Roommates Problem Further Stable Matching Problems Other Optimal Matching Problems: Pareto Optimal Matchings Popular Matchings Profile-Based Optimal Matchings.

/pdf/algorithmics-of-matching-under-preferences-2l3a9z5euq.pdf

Algorithmics of Matching Under Preferences

Wherefore art thou R3579X?: anonymized social networks, hidden patterns, and structural steganography

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

/pdf/handbook-of-computational-social-choice-12i1xbv1b8.pdf

Handbook of Computational Social Choice

https://people.mpi-inf.mpg.de/~mehlhorn/ftp/SurveyCycleBases.pdf

Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications

We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a nonempty subset of posts in order of preference, possibly involving ties. We say that a matching $M$ is popular if there is no matching $M'$ such that the number of applicants preferring $M'$ to $M$ exceeds the number of applicants preferring $M$ to $M'$. In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching and to find a largest such matching, if one exists. For the special case in which every preference list is strictly ordered (i.e., contains no ties), we give an $O(n + m)$ time algorithm, where $n$ is the total number of applicants and posts and $m$ is the total length of all of the preference lists. For the general case in which preference lists may contain ties, we give an $O(\sqrt{n}m)$ time algorithm.

Popular Matchings

An (α, β)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of α and an additive term β. It is well known that any graph contains a (multiplicative) (2k−1, 0)-spanner of size O(n1+1/k) and an (additive) (1,2)-spanner of size O(n3/2). However no other additive spanners are known to exist.In this article we develop a couple of new techniques for constructing (α, β)-spanners. Our first result is an additive (1,6)-spanner of size O(n4/3). The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which (α, β)-spanners can be computed efficiently, ideally in linear time. We show that, for any k, a (k,k−1)-spanner with size O(kn1+1/k) can be found in linear time, and, further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.

/pdf/additive-spanners-and-a-b-spanners-3mh1j35rfy.pdf

Additive spanners and (α, β)-spanners

We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly involving ties. We say that a matching M is popular if there is no matching M' such that the number of applicants preferring M' to M exceeds the number of applicants preferring M to M'. In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists. For the special case in which every preference list is strictly ordered (i.e. contains no ties), we give an O(n+m) time algorithm, where n is the total number of applicants and posts, and m is the total length of all the preference lists. For the general case in which preference lists may contain ties, we give an O(√nm) time algorithm, and show that the problem has equivalent time complexity to the maximum-cardinality bipartite matching problem.

Popular matchings

http://www.cse.iitm.ac.in/~meghana/papers/TCS11-2.pdf

Telikepalli Kavitha

Papers

Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications

Popular Matchings

Additive spanners and (α, β)-spanners

Popular matchings

Popular mixed matchings