Center for Discrete Mathematics and Theoretical Computer Science

About: Center for Discrete Mathematics and Theoretical Computer Science is a facility organization based out in Piscataway, New Jersey, United States. It is known for research contribution in the topics: Local search (optimization) & Optimization problem. The organization has 140 authors who have published 175 publications receiving 2345 citations.

Late Breaking Results: An Analytical Timing-Driven Placer for Heterogeneous FPGAs *

Abstract: As the feature sizes keep shrinking, interconnect delays have become a major limiting factor for FPGA timing closure. Traditional placement algorithms that address wirelength alone are no longer sufficient to close timing, especially for the large-scale heterogeneous FPGAs. In this paper, we resolve the crucial FPGA placement problem by optimizing wirelength and timing simultaneously. First, a smoothed routing-architecture-aware timing model is proposed to accurately estimate each interconnect delay. Then, a timing-driven delay look-up table is constructed to further speed up delay access. Finally, we present an effective wirelength and timing co-optimization strategy to produce high-quality placements without timing violations. Compared with Vivado 2019.1 on Xilinx benchmark suites for xc7k325t device, experimental results show that our algorithm achieves not only a 6.6% improvement in worst slack but also a 3.2% reduction for routed wirelength.

A Steiner point candidate-based heuristic framework for the Steiner tree problem in graphs

Abstract: The underlying models of many practical problems in various engineering fields are equivalent to the Steiner tree problem in graphs, which is a typical NP-hard combinatorial optimization problem. Thus, developing a fast and effective heuristic for the Steiner tree problem in graphs is of universal significance. By analyzing the advantages and disadvantages of the fast classic heuristics, we find that the shortest paths and Steiner points play important roles in solving the Steiner tree problem in graphs. Based on the analyses, we propose a Steiner point candidate-based heuristic algorithm framework (SPCF) for solving the Steiner tree problem in graphs. SPCF consists of four stages: marking SPCI points, constructing the Steiner tree, eliminating the detour paths, and SPCII-based refining stage. For each procedure of SPCF, we present several alternative strategies to make the trade-off between the effectiveness and efficiency of the algorithm. By finding the shortest path clusters between vertex sets, sever...

Optimal US coast guard boat allocations with sharing

Abstract: The United States Coast Guard (USCG) presently allocates resources, such as small boats, to fixed locations (stations) for periods of one year or longer. We present a model that allows the USCG to assess novel boat allocations in which stations may “share” boats, thus cutting down on the total number of boats required. A shared boat is assigned to one particular station for each sub-portion of the year. A key innovation of the analysis is to characterize the problem in terms of “sharing paths,” rather than modeling individual boats. The model uses Mixed Integer Programming to capture a subtle set of constraints and business rules such as boat and mission requirements for individual stations, preferred amount of usage (mission hours) for the boats, and limitations on how much sharing should be allowed. The model finds a boat assignment plan (with sharing) that can minimize either the number of boats or the total cost, subject to these various constraints. The scale of operations that is meaningful to the USCG permits adequate solutions to be found on a large laptop computer.

A homogeneous polynomial associated with general hypergraphs and its applications.

Abstract: In this paper, we define a homogeneous polynomial for a general hypergraph, and establish a remarkable connection between clique number and the homogeneous polynomial of a general hypergraph. For a general hypergraph, we explore some inequality relations among spectral radius, clique number and the homogeneous polynomial. We also give lower and upper bounds on the spectral radius in terms of the clique number.