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职业迁徙
个人简介
I work in the intersection of theoretical computer science and discrete mathematics. In particular, currently I am interested in approximation algorithms, discrepancy theory and related questions in high dimensional convex geometry. Here is some recent work:
Approximation algorithms. For many problems, the naive linear programming relaxation is too weak to find good approximations. The Sherali-Adams / Lasserre lift then provides a systematic strengthening. For example in [Davies et al. FOCS 2020] we can use this method to obtain a O(log^2 n)-approximation for scheduling with precedence constraints and communication delays.
Discrepancy theory. In the geometric setting of discrepancy theory, one has a concrete symmetric convex body K and asks for a minimal scaling of s > 0, so that the body sK contains a vector with {-1,+1} entries. In [Reis, R. SODA 2020], we considered the body K arising from balancing matrices w.r.t. the operator norm and prove that it must have high mean width. Then this implies a new algorithm to find linear-size spectral sparsifiers in graphs.
Approximation algorithms. For many problems, the naive linear programming relaxation is too weak to find good approximations. The Sherali-Adams / Lasserre lift then provides a systematic strengthening. For example in [Davies et al. FOCS 2020] we can use this method to obtain a O(log^2 n)-approximation for scheduling with precedence constraints and communication delays.
Discrepancy theory. In the geometric setting of discrepancy theory, one has a concrete symmetric convex body K and asks for a minimal scaling of s > 0, so that the body sK contains a vector with {-1,+1} entries. In [Reis, R. SODA 2020], we considered the body K arising from balancing matrices w.r.t. the operator norm and prove that it must have high mean width. Then this implies a new algorithm to find linear-size spectral sparsifiers in graphs.
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2023 IEEE 64TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, FOCSpp.1292-1300, (2023)
CoRR (2023)
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2023 IEEE 64TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, FOCS (2023): 974-988
CoRR (2023)
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arxiv(2023)
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arxiv(2022)
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