Connected Coordination: Network Structure and Group Coordination

Networks can affect a group’s ability to solve a coordination problem. We utilize laboratory experiments to study the conditions under which groups of subjects can solve coordination games. We investigate a variety of different network structures, and we also investigate coordination games with symmetric and asymmetric payoffs. Our results show that network connections facilitate coordination in both symmetric and asymmetric games. Most significantly, we find that increases in the number of network connections encourage coordination even when payoffs are highly asymmetric. These results shed light on the conditions that may facilitate coordination in real-world networks

Effect of connectivity in an associative memory model

AbstractWe investigate how geometric properties translate into functional properties in sparse networks of computing elements. Specifically, we determine how the eigenvalues of the interconnection graph (which in turn reflect connectivity properties) relate to the quantities, number of items stored, amount of error-correction, radius of attraction, and rate of convergence, in an associative memory model consisting of a sparse network of threshold elements or neurons

On the Fine-Grained Complexity of One-Dimensional Dynamic Programming

In this paper, we investigate the complexity of one-dimensional dynamic programming, or more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of n data items together with weights for every pair of the items, the task is to determine a subsequence S minimizing the total weight of the pairs adjacent in S. A large number of natural problems can be formulated as LWS problems, yielding obvious O(n^2)-time solutions. In many interesting instances, the O(n^2)-many weights can be succinctly represented. Yet except for near-linear time algorithms for some specific special cases, little is known about when an LWS instantiation admits a subquadratic-time algorithm and when it does not. In particular, no lower bounds for LWS instantiations have been known before. In an attempt to remedy this situation, we provide a general approach to study the fine-grained complexity of succinct instantiations of the LWS problem: Given an LWS instantiation we identify a highly parallel core problem that is subquadratically equivalent. This provides either an explanation for the apparent hardness of the problem or an avenue to find improved algorithms as the case may be. More specifically, we prove subquadratic equivalences between the following pairs (an LWS instantiation and the corresponding core problem) of problems: a low-rank version of LWS and minimum inner product, finding the longest chain of nested boxes and vector domination, and a coin change problem which is closely related to the knapsack problem and (min,+)-convolution. Using these equivalences and known SETH-hardness results for some of the core problems, we deduce tight conditional lower bounds for the corresponding LWS instantiations. We also establish the (min,+)-convolution-hardness of the knapsack problem. Furthermore, we revisit some of the LWS instantiations which are known to be solvable in near-linear time and explain their easiness in terms of the easiness of the corresponding core problems

0-1 Integer Linear Programming with a Linear Number of Constraints

We give an exact algorithm for the 0-1 Integer Linear Programming problem with a linear number of constraints that improves over exhaustive search by an exponential factor. Specifically, our algorithm runs in time $2^{(1-\text{poly}(1/c))n}$ where n is the number of variables and cn is the number of constraints. The key idea for the algorithm is a reduction to the Vector Domination problem and a new algorithm for that subproblem