# Seminar: Danish Kashaev (CWI) and Arash Pourdamghani (TU Berlin), 2 PhD-talks

Speaker: Danish Kashaev (CWI) and Arash Pourdamghani (TU Berlin)

Title:

Danish Kashaev: Round and Bipartize for Vertex Cover Approximation

Arash Pourdamghani: SeedTree: A Dynamically Optimal and Local Self-Adjusting Tree

https://cwi-nl.zoom.us/j/84909645595?pwd=b1M4QnNKVzNMdmNSVFNaZUJmR1kvUT09
(Meeting ID: 849 0964 5595, Passcode: 772448)

Abstract of "Round and Bipartize for Vertex Cover Approximation" (Danish Kashaev):
The vertex cover problem is a fundamental and widely studied NP-Hard combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a consequence, the natural rounding algorithm based on this relaxation computes an optimal solution for bipartite graphs and a 2-approximation for general graphs. This 2-approximation cannot be improved in the worst-case if the unique games conjecture is true.

In this talk, we present a simple rounding algorithm based on the standard relaxation which has additional access to an odd cycle transversal (i.e. a set of vertices whose removal leaves the graph bipartite) and analyze its approximation guarantee. The motivation for studying this setting comes from an interest in interpolating the rounding curve of the standard LP in a beyond the worst-case manner, depending on how close the graph is to being bipartite. A key parameter determining tight bounds on the approximation ratio turns out to be the odd girth of the graph, defined as the length of the shortest odd cycle. We also show optimality of the analysis and discuss algorithmic applications in order to find good odd cycle transversals.

Based on https://arxiv.org/abs/2211.01699.

Video of the talk of Danish Kashaev:

Slides of the talk of Danish Kashaev:
Slides

Abstract of "SeedTree: A Dynamically Optimal and Local Self-Adjusting Tree" (Arash Pourdamghani):
The vision of developing self-adjusting networks is now a reality: programmable optical networking switches are already being used
in big tech companies such as Google and Microsoft. However, theoretical foundations are lagging behind in this area: previous methods have been designed by having fixed and limited networking resources in mind. In this talk, I first describe how we can go from self-adjusting trees to self-adjusting networks, and then focus on the new model that we are proposing that has two key differences from traditional self-adjusting trees: it allows for capacities higher than one per node, and it uses item movements instead of rotation. Given this novel model, I detail how to design a randomized constant competitive algorithm that also allows for greedy local routing. Hence the cost of our algorithm is asymptotically optimal given any input demand while ensuring local adjustments and routing.

Based on https://arxiv.org/pdf/2301.03074.

Video of the talk of Arash Pourdamghani:

Slides of the talk of Arash Pourdamghani:
Slides