# Symbolic Graphs: Linear Solutions to Connectivity Related Problems

@article{Gentilini2007SymbolicGL, title={Symbolic Graphs: Linear Solutions to Connectivity Related Problems}, author={Raffaella Gentilini and Carla Piazza and Alberto Policriti}, journal={Algorithmica}, year={2007}, volume={50}, pages={120-158} }

Abstract
The importance of symbolic data structures such as Ordered Binary Decision Diagrams (OBDD) is rapidly growing in many areas of Computer Science where the large dimensions of the input models is a challenging feature: OBDD based graph representations allowed to define truly new standards in the achievable dimensions for the Model Checking verification technique. However, OBDD representations pose strict constraints in the algorithm design issue. For example, Depth-First Search (DFS) is…

## 28 Citations

### Symbolic OBDD-Based Reachability Analysis Needs Exponential Space

- Computer Science, MathematicsSOFSEM
- 2010

An exponential lower bound on the space complexity of an arbitrary OBDD-based algorithm for the reachability problem is presented and a general exponentialLower bound is obtained for the computation of OBDDs representing all connected node pairs in a graph, the transitive closure.

### Exponential Space Complexity for Symbolic Maximum Flow Algorithms in 0-1 Networks

- Computer ScienceMFCS
- 2010

The first exponential lower bound on the space complexity of OBDD-based algorithms for the maximum flow problem in 0-1 networks is presented.

### On symbolic OBDD-based algorithms for the minimum spanning tree problem

- Computer Science, MathematicsTheor. Comput. Sci.
- 2010

### On Symbolic Representations of Maximum Matchings and (Un)directed Graphs

- Computer Science, MathematicsIFIP TCS
- 2010

It is shown that symbolic OBDD-based algorithms for the maximum matching problem need exponential space (with respect to the O BDD size of the input graph) and it is shown That OBDd-representations for undirected graphs can be exponentially larger than OBD D-representation for their directed counterparts and vice versa.

### Lower Bounds for Symbolic Computation on Graphs: Strongly Connected Components, Liveness, Safety, and Diameter

- Computer Science, MathematicsSODA
- 2018

Lower bounds on the number of symbolic operations are given for basic graph problems such as the computation of the strongly connected components and of the approximate diameter as well as for fundamental problems in model checking such as safety, liveness, and co-liveness.

### On the OBDD representation of some graph classes

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2016

### Exponential space complexity for OBDD-based reachability analysis

- Computer Science, MathematicsInf. Process. Lett.
- 2010

### OBDD-Based Representation of Interval Graphs

- Computer ScienceWG
- 2013

This paper shows that the OBDD size of unit interval graphs is O( ∣ V ∣ /log ∣ v ∣ ) and theOBDD sizes of interval graphs are O(∣V ∣ log∣ V∣ ) which both improve a known result from Nunkesser and Woelfel (2009) and can be provable small for special graph classes.

### Symbolic Time and Space Tradeoffs for Probabilistic Verification

- Computer Science, Mathematics2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2021

A faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs) and considers the canonical parity objectives for ω-regular objectives.

### BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

- Computer Science, MathematicsLog. Methods Comput. Sci.
- 2022

A novel algorithm is proposed that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph and uses it to explore the SCCs of a large collection of coloured graphs obtained from Boolean networks – a modelling framework commonly appearing in systems biology.

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