We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

Triangulating a simple polygon in linear time

Graph Theory with Applications to Engineering and Computer ... This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra.

Graph theory with applications to engineering and computer science, by Narsingh Deo. Pp xvii, 478. 1974. SBN 0 13 363473 6 (Prentice-Hall)

Software-defined networking (SDN) is an emerging architecture used in many applications because of its flexible architecture. It is expected to become an essential enabler for the Internet of Things (IoTs). It decouples the control plane from the data plane, and the controller manages the whole underlying network. SDN has been used in wireless sensor networks (WSNs) for routing. The SDN controller uses some algorithms to calculate the routing path; however, none of these algorithms have enough ability to obtain the optimized routing path. Therefore, reinforcement learning (RL) is a helpful technique to select the best routing path. In this article, we optimize the routing path of SDWSN through RL. A reward function is proposed that includes all required metrics regarding energy efficiency and network Quality-of-Service (QoS). The agent gets the reward and takes the next action based on the reward received, while the SDWSN controller improves the routing path based on the previous experience. However, the whole network is also controlled remotely through the Web. The performance of the RL-based SDWSN is compared with SDN-based techniques, including traditional SDN and energy-aware SDN (EASDN), QR-SDN, TIDE and non SDN-based techniques, such as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning and RL-based routing (RLBR). The proposed RL-based SDWSN outperforms in terms of lifetime from 8% to 33% and packet delivery ratio (PDR) from 2% to 24%. It is envisioned that this work will help the engineers for achieving the desired WSN performance through efficient routing. 

Improving the Software-Defined Wireless Sensor Networks Routing Performance Using Reinforcement Learning

Circuit routing is a fundamental problem in designing electronic systems such as integrated circuits (ICs) and printed circuit boards (PCBs) which form the hardware of electronics and computers. Like finding paths between pairs of locations, circuit routing generates traces of wires to connect contacts or leads of circuit components. It is challenging because finding paths between dense and massive electronic components involves a very large search space. Existing solutions are either manually designed with domain knowledge or tailored to specific design rules, hence, difficult to adapt to new problems or design needs. Therefore, a general routing approach is highly desired. In this paper, we model the circuit routing as a sequential decision-making problem, and solve it by Monte Carlo tree search (MCTS) with deep neural network (DNN) guided rollout. It could be easily extended to routing cases with more routing constraints and optimization goals. Experiments on randomly generated single-layer circuits show the potential to route complex circuits. The proposed approach can solve the problems that benchmark methods such as sequential A* method and Lee's algorithm cannot solve, and can also outperform the vanilla MCTS approach.

Circuit Routing Using Monte Carlo Tree Search and Deep Neural Networks.

The guard zone computation problem finds vast applications in the field of VLSI physical design automation and design of embedded systems, where one of the major purposes is to find an optimized way to place a set of 2D blocks on a chip floor. In VLSI layout design, the circuit components (or the functional units/modules or groups/blocks of different subcircuits) are not supposed to be placed much closer to each other in order to avoid electrical (parasitic) effects among them (http://en.wikipedia.org/wiki/Curve_orientation, [13]). The (group of) circuit components on a chip floor may be viewed as a set of polygonal regions on a two-dimensional plane. Each (group of) circuit component(s) C i is associated with a parameter δ i such that a minimum clearance zone of width δ i is to be maintained around C i . The regions representing the (groups of) circuit components are in general isothetic polygons, but may not always be limited to convex ones. The location of the guard zone (of specified width) for a simple polygon is a very important problem for resizing the (group of) circuit components. In this paper, we have developed an algorithm to compute the guard zone of a simple polygon as well as to exclude the overlapped regions among the guard zones, if any. If the number of vertices in the given polygon is n, then our algorithm requires O(n log n + I log n) time, where I is the number of intersections among the guard zones. So, it is output sensitive in nature that depends on the value of δ i . The algorithm developed in the paper is proved to report a preferred guard zone of the given simple polygon excluding all the intersections, if any.

A 2D Guard Zone Computation Algorithm for Reassignment of Subcircuits to Minimize the Overall Chip Area

Generation of all possible spanning trees of a graph is a major area of research in graph theory as the number of spanning trees of a graph increases exponentially with graph size. Several algorithms of varying 
efficiency have been developed since early 1960s by researchers around the globe. This article is an exhaustive literature survey on these algorithms, assuming the input to be a simple undirected connected graph of finite order, and contains detailed analysis and comparisons in both theoretical and experimental behavior of these algorithms.

/pdf/algorithms-for-generating-all-possible-spanning-trees-of-a-29k31wmte9.pdf

Algorithms for generating all possible spanning trees of a simple undirected connected graph: an extensive review

Given a simple polygon P, its guard zone G (of width r) is a closed region consisting of straight line segments and circular arcs (of radius r) bounding the polygon P such that there exists no pair of points p (on the boundary of P) and q (on the boundary of G) having their Euclidean distance d(p,q) less than r. In this paper we have designed a time-optimal sequential algorithm to solve the guard zone problem.

A time-optimal algorithm for guard zone problem

Given a simple polygon P , its guard zone G (of width r ) is a closed region consisting of straight line segments and circular arcs (of radius r ) bounding the polygon P such that there exists no pair of points p (on the boundary of P ) and q (on the boundary of G ) having their Euclidean distance d (p ,q ) less than r . In this paper we have designed a time-optimal sequential algorithm to solve the guard zone problem, and developed a cost-optimal parallel counterpart of the same problem for solving it in distributed environment.

A Cost-Optimal Algorithm for Guard Zone Problem

Channel routing and crosstalk minimization are important issues while we talk about high-performance circuits for VLSI physical design automation. Interconnection among the net terminals satisfying constraints in an intelligent way is a necessity to realize a circuit in a minimum possible area, as this is a primary requirement to reduce cost as well as to increase yield. In this paper, along with area minimization, the performance of the computed circuits has also been enhanced by computing routing solutions with a specified amount of bottleneck crosstalk in two-layer channel routing. Usually, crosstalk is measured by the amount of overlapping of a pair of nets assigned to adjacent tracks. The crosstalk minimization problem in the reserved two-layer Manhattan channel routing model is NP-hard. Thus, in this paper, heuristic algorithms have been devised to optimize bottleneck crosstalk in order to augment circuit performance in two-layer channel routing. Experimental results obtained are highly encouraging.

Ranjan Mehera

Papers

Algorithms for generating all possible spanning trees of a simple undirected connected graph: an extensive review

A time-optimal algorithm for guard zone problem

A Cost-Optimal Algorithm for Guard Zone Problem

A 2D Guard Zone Computation Algorithm for Reassignment of Subcircuits to Minimize the Overall Chip Area

Algorithms for Minimizing Bottleneck Crosstalk in Two-Layer Channel Routing